{"id":2878,"date":"2026-10-29T09:38:41","date_gmt":"2026-10-29T02:38:41","guid":{"rendered":"https:\/\/navi.edu.vn\/blog\/?p=2878"},"modified":"2026-10-29T09:38:41","modified_gmt":"2026-10-29T02:38:41","slug":"de-cuong-on-tap-giua-ki-1-toan-8","status":"publish","type":"post","link":"https:\/\/navi.edu.vn\/blog\/de-cuong-on-tap-giua-ki-1-toan-8\/","title":{"rendered":"\u0110\u1ec1 c\u01b0\u01a1ng \u00f4n t\u1eadp gi\u1eefa k\u00ec 1 To\u00e1n 8 (2026-2027) &#038; \u0110\u1ec1 thi m\u1eabu c\u00f3 \u0111\u00e1p \u00e1n"},"content":{"rendered":"<div class=\"naviedu-intro-section\" style=\"font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif; line-height: 1.8; color: #2d3748; font-size: 16px;\">\n<p>L\u1edbp 8 l\u00e0 n\u0103m h\u1ecdc b\u1ea3n l\u1ec1 mang t\u00ednh quy\u1ebft \u0111\u1ecbnh \u0111\u1eb7t n\u1ec1n m\u00f3ng cho k\u1ef3 thi tuy\u1ec3n sinh v\u00e0o l\u1edbp 10 v\u1edbi c\u00e1c chuy\u00ean \u0111\u1ec1 \u0111\u1ea1i s\u1ed1 v\u00e0 h\u00ecnh h\u1ecdc c\u00f3 \u0111\u1ed9 kh\u00f3 t\u0103ng v\u1ecdt. Vi\u1ec7c s\u1edf h\u1eefu m\u1ed9t b\u1ea3n <strong>\u0111\u1ec1 c\u01b0\u01a1ng \u00f4n t\u1eadp gi\u1eefa k\u00ec 1 to\u00e1n 8<\/strong> chu\u1ea9n h\u00f3a gi\u00fap h\u1ecdc sinh v\u01b0\u1ee3t qua nh\u1eefng n\u1ed7i \u0111au th\u01b0\u1eddng g\u1eb7p nh\u01b0 nh\u1ea7m d\u1ea5u khi khai tri\u1ec3n h\u1eb1ng \u0111\u1eb3ng th\u1ee9c, kh\u00f4ng nh\u1eadn di\u1ec7n \u0111\u01b0\u1ee3c d\u1ea1ng th\u1ee9c \u0111\u1ec3 ph\u00e2n t\u00edch \u0111a th\u1ee9c th\u00e0nh nh\u00e2n t\u1eed hay l\u00fang t\u00fang khi ch\u1ee9ng minh c\u00e1c t\u1ee9 gi\u00e1c \u0111\u1eb7c bi\u1ec7t.<\/p>\n<p>Hi\u1ec3u \u0111\u01b0\u1ee3c nh\u1eefng th\u1eed th\u00e1ch \u0111\u00f3, NaviEdu g\u1eedi t\u1eb7ng tr\u1ecdn b\u1ed9 t\u00e0i li\u1ec7u \u00f4n t\u1eadp to\u00e0n di\u1ec7n: h\u1ec7 th\u1ed1ng l\u00fd thuy\u1ebft tr\u1ecdng t\u00e2m, ph\u01b0\u01a1ng ph\u00e1p gi\u1ea3i chi ti\u1ebft, l\u1ecbch \u00f4n t\u1eadp 7 ng\u00e0y khoa h\u1ecdc v\u00e0 \u0111\u1ec1 thi m\u1eabu c\u00f3 \u0111\u00e1p \u00e1n gi\u00fap con t\u1ef1 tin b\u1ee9t ph\u00e1 \u0111i\u1ec3m s\u1ed1.<\/p>\n<\/div>\n<figure style=\"margin: 24px 0; text-align: center;\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-2879\" style=\"max-width: 100%; height: auto; border-radius: 10px;\" src=\"https:\/\/navi.edu.vn\/blog\/wp-content\/uploads\/2026\/10\/de-cuong-on-tap-giua-ki-1-toan-8-tom-tat.png\" alt=\"\u0110\u1ec1 c\u01b0\u01a1ng \u00f4n t\u1eadp gi\u1eefa k\u00ec 1 To\u00e1n 8 \u2013 t\u00f3m t\u1eaft ki\u1ebfn th\u1ee9c tr\u1ecdng t\u00e2m\" width=\"1200\" height=\"760\" srcset=\"https:\/\/navi.edu.vn\/blog\/wp-content\/uploads\/2026\/10\/de-cuong-on-tap-giua-ki-1-toan-8-tom-tat.png 1200w, https:\/\/navi.edu.vn\/blog\/wp-content\/uploads\/2026\/10\/de-cuong-on-tap-giua-ki-1-toan-8-tom-tat-300x190.png 300w, https:\/\/navi.edu.vn\/blog\/wp-content\/uploads\/2026\/10\/de-cuong-on-tap-giua-ki-1-toan-8-tom-tat-1024x649.png 1024w, https:\/\/navi.edu.vn\/blog\/wp-content\/uploads\/2026\/10\/de-cuong-on-tap-giua-ki-1-toan-8-tom-tat-768x486.png 768w\" sizes=\"(max-width: 1200px) 100vw, 1200px\" \/><figcaption style=\"font-size: 14px; color: #718096; margin-top: 8px;\">S\u01a1 \u0111\u1ed3 t\u00f3m t\u1eaft \u0111\u1ec1 c\u01b0\u01a1ng \u00f4n t\u1eadp gi\u1eefa k\u00ec 1 To\u00e1n 8 (2026\u20132027)<\/figcaption><\/figure>\n<div class=\"naviedu-toc\" style=\"background: #f7fafc; border: 1px solid #e2e8f0; border-radius: 8px; padding: 16px 22px; margin: 24px 0;\">\n<p style=\"margin: 0 0 8px 0; font-weight: bold; color: #0056b3; font-size: 17px;\">M\u1ee5c l\u1ee5c \u0111\u1ec1 c\u01b0\u01a1ng \u00f4n t\u1eadp gi\u1eefa k\u00ec 1 To\u00e1n 8<\/p>\n<ul style=\"margin: 0; padding-left: 22px; line-height: 1.9;\">\n<li style=\"font-weight: bold; list-style-type: disc;\"><a style=\"color: #2d3748; text-decoration: none;\" href=\"#muc-1-cau-truc-de-thi-giua-ki-1-toan-8-theo-thong-tu-22\">C\u1ea5u tr\u00fac \u0111\u1ec1 thi gi\u1eefa k\u00ec 1 To\u00e1n 8 theo Th\u00f4ng t\u01b0 22<\/a><\/li>\n<li style=\"font-weight: bold; list-style-type: disc;\"><a style=\"color: #2d3748; text-decoration: none;\" href=\"#muc-2-phan-i-da-thuc-va-hang-dang-thuc\">Ph\u1ea7n I: \u0110a Th\u1ee9c v\u00e0 H\u1eb1ng \u0110\u1eb3ng Th\u1ee9c<\/a><\/li>\n<li style=\"font-weight: normal; margin-left: 14px; list-style-type: circle;\"><a style=\"color: #2d3748; text-decoration: none;\" href=\"#muc-3-don-thuc\">\u0110\u01a1n th\u1ee9c<\/a><\/li>\n<li style=\"font-weight: normal; margin-left: 14px; list-style-type: circle;\"><a style=\"color: #2d3748; text-decoration: none;\" href=\"#muc-4-da-thuc-nhieu-bien\">\u0110a th\u1ee9c nhi\u1ec1u bi\u1ebfn<\/a><\/li>\n<li style=\"font-weight: normal; margin-left: 14px; list-style-type: circle;\"><a style=\"color: #2d3748; text-decoration: none;\" href=\"#muc-5-cong-tru-nhan-da-thuc\">C\u1ed9ng, tr\u1eeb, nh\u00e2n \u0111a th\u1ee9c<\/a><\/li>\n<li style=\"font-weight: normal; margin-left: 14px; list-style-type: circle;\"><a style=\"color: #2d3748; text-decoration: none;\" href=\"#muc-6-chia-da-thuc-cho-don-thuc\">Chia \u0111a th\u1ee9c cho \u0111\u01a1n th\u1ee9c<\/a><\/li>\n<li style=\"font-weight: normal; margin-left: 14px; list-style-type: circle;\"><a style=\"color: #2d3748; text-decoration: none;\" href=\"#muc-7-hang-dang-thuc-dang-nho\">H\u1eb1ng \u0111\u1eb3ng th\u1ee9c \u0111\u00e1ng nh\u1edb<\/a><\/li>\n<li style=\"font-weight: normal; margin-left: 14px; list-style-type: circle;\"><a style=\"color: #2d3748; text-decoration: none;\" href=\"#muc-8-phan-tich-da-thuc-thanh-nhan-tu\">Ph\u00e2n t\u00edch \u0111a th\u1ee9c th\u00e0nh nh\u00e2n t\u1eed<\/a><\/li>\n<li style=\"font-weight: normal; margin-left: 14px; list-style-type: circle;\"><a style=\"color: #2d3748; text-decoration: none;\" href=\"#muc-9-chung-minh-bieu-thuc-khong-phu-thuoc-vao-bien\">Ch\u1ee9ng minh bi\u1ec3u th\u1ee9c kh\u00f4ng ph\u1ee5 thu\u1ed9c v\u00e0o bi\u1ebfn<\/a><\/li>\n<li style=\"font-weight: bold; list-style-type: disc;\"><a style=\"color: #2d3748; text-decoration: none;\" href=\"#muc-10-phan-ii-tu-giac\">Ph\u1ea7n II: T\u1ee9 Gi\u00e1c<\/a><\/li>\n<li style=\"font-weight: normal; margin-left: 14px; list-style-type: circle;\"><a style=\"color: #2d3748; text-decoration: none;\" href=\"#muc-11-tu-giac\">T\u1ee9 gi\u00e1c<\/a><\/li>\n<li style=\"font-weight: normal; margin-left: 14px; list-style-type: circle;\"><a style=\"color: #2d3748; text-decoration: none;\" href=\"#muc-12-hinh-thang-can\">H\u00ecnh thang c\u00e2n<\/a><\/li>\n<li style=\"font-weight: normal; margin-left: 14px; list-style-type: circle;\"><a style=\"color: #2d3748; text-decoration: none;\" href=\"#muc-13-hinh-binh-hanh\">H\u00ecnh b\u00ecnh h\u00e0nh<\/a><\/li>\n<li style=\"font-weight: normal; margin-left: 14px; list-style-type: circle;\"><a style=\"color: #2d3748; text-decoration: none;\" href=\"#muc-14-hinh-chu-nhat\">H\u00ecnh ch\u1eef nh\u1eadt<\/a><\/li>\n<li style=\"font-weight: normal; margin-left: 14px; list-style-type: circle;\"><a style=\"color: #2d3748; text-decoration: none;\" href=\"#muc-15-hinh-thoi-hinh-vuong\">H\u00ecnh thoi, h\u00ecnh vu\u00f4ng<\/a><\/li>\n<li style=\"font-weight: bold; list-style-type: disc;\"><a style=\"color: #2d3748; text-decoration: none;\" href=\"#muc-16-phan-iii-lich-on-tap-7-ngay-de-thi-mau\">Ph\u1ea7n III: L\u1ecbch \u00d4n T\u1eadp 7 Ng\u00e0y &amp; \u0110\u1ec1 Thi M\u1eabu<\/a><\/li>\n<li style=\"font-weight: normal; margin-left: 14px; list-style-type: circle;\"><a style=\"color: #2d3748; text-decoration: none;\" href=\"#muc-17-lich-on-tap-giua-ki-1-toan-8-trong-7-ngay-giup-con-tu-tin-da\">L\u1ecbch \u00f4n t\u1eadp gi\u1eefa k\u00ec 1 To\u00e1n 8 trong 7 ng\u00e0y gi\u00fap con t\u1ef1 tin \u0111\u1ea1t \u0111i\u1ec3m cao<\/a><\/li>\n<li style=\"font-weight: normal; margin-left: 14px; list-style-type: circle;\"><a style=\"color: #2d3748; text-decoration: none;\" href=\"#muc-18-tai-de-cuong-on-tap-giua-ki-1-toan-8-va-de-thi-mau-pdf-co-da\">T\u1ea3i \u0111\u1ec1 c\u01b0\u01a1ng \u00f4n t\u1eadp gi\u1eefa k\u00ec 1 To\u00e1n 8 v\u00e0 \u0111\u1ec1 thi m\u1eabu (PDF c\u00f3 \u0111\u00e1p \u00e1n)<\/a><\/li>\n<li style=\"font-weight: bold; list-style-type: disc;\"><a style=\"color: #2d3748; text-decoration: none;\" href=\"#muc-19-loi-ket\">L\u1eddi k\u1ebft<\/a><\/li>\n<\/ul>\n<\/div>\n<p><!-- B\u1eaeT \u0110\u1ea6U: C\u1ea4U TR\u00daC \u0110\u1ec0 THI GI\u1eeeA K\u00cc 1 TO\u00c1N 8 --><\/p>\n<div class=\"naviedu-content-section\" style=\"font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif; line-height: 1.8; color: #2d3748; font-size: 16px;\">\n<h2 id=\"muc-1-cau-truc-de-thi-giua-ki-1-toan-8-theo-thong-tu-22\" style=\"color: #0056b3; border-bottom: 2px solid #e2e8f0; padding-bottom: 8px; margin-top: 30px; font-size: 22px;\">C\u1ea5u tr\u00fac \u0111\u1ec1 thi gi\u1eefa k\u00ec 1 To\u00e1n 8 theo Th\u00f4ng t\u01b0 22<\/h2>\n<figure id=\"attachment_2906\" aria-describedby=\"caption-attachment-2906\" style=\"width: 800px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-2906\" src=\"https:\/\/navi.edu.vn\/blog\/wp-content\/uploads\/2026\/10\/de-cuong-on-tap-giua-ki-1-toan-8-300x188.png\" alt=\"T\u00ecm hi\u1ec3u v\u1ec1 c\u1ea5u tr\u00fac ma tr\u1eadn \u0111\u1ec1 thi gi\u1eefa k\u1ef3 1 To\u00e1n 8\" width=\"800\" height=\"500\" srcset=\"https:\/\/navi.edu.vn\/blog\/wp-content\/uploads\/2026\/10\/de-cuong-on-tap-giua-ki-1-toan-8-300x188.png 300w, https:\/\/navi.edu.vn\/blog\/wp-content\/uploads\/2026\/10\/de-cuong-on-tap-giua-ki-1-toan-8-1024x640.png 1024w, https:\/\/navi.edu.vn\/blog\/wp-content\/uploads\/2026\/10\/de-cuong-on-tap-giua-ki-1-toan-8-768x480.png 768w, https:\/\/navi.edu.vn\/blog\/wp-content\/uploads\/2026\/10\/de-cuong-on-tap-giua-ki-1-toan-8-1536x961.png 1536w, https:\/\/navi.edu.vn\/blog\/wp-content\/uploads\/2026\/10\/de-cuong-on-tap-giua-ki-1-toan-8.png 1586w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><figcaption id=\"caption-attachment-2906\" class=\"wp-caption-text\">T\u00ecm hi\u1ec3u v\u1ec1 c\u1ea5u tr\u00fac ma tr\u1eadn \u0111\u1ec1 thi gi\u1eefa k\u1ef3 1 To\u00e1n 8<\/figcaption><\/figure>\n<p>H\u1ecdc sinh c\u1ea5p THCS \u0111\u01b0\u1ee3c \u0111\u00e1nh gi\u00e1 k\u1ebft qu\u1ea3 h\u1ecdc t\u1eadp theo <a href=\"https:\/\/luatvietnam.vn\/giao-duc\/thong-tu-22-2021-tt-bgddt-207846-d1.html\" target=\"_blank\" rel=\"noopener\">Th\u00f4ng t\u01b0 22\/2021\/TT-BGD\u0110T<\/a>. B\u00e0i ki\u1ec3m tra \u0111\u1ecbnh k\u00ec gi\u1eefa h\u1ecdc k\u00ec 1 m\u00f4n To\u00e1n l\u1edbp 8 th\u01b0\u1eddng c\u00f3 th\u1eddi gian l\u00e0m b\u00e0i l\u00e0 <strong>90 ph\u00fat<\/strong>. V\u00ec ma tr\u1eadn, b\u1ea3n \u0111\u1eb7c t\u1ea3 v\u00e0 \u0111\u1ec1 ki\u1ec3m tra ch\u00ednh th\u1ee9c do t\u1ed5 chuy\u00ean m\u00f4n c\u1ee7a t\u1eebng tr\u01b0\u1eddng THCS t\u1ef1 x\u00e2y d\u1ef1ng (\u0111\u1eb7c bi\u1ec7t hi\u1ec7n nay m\u1ed9t s\u1ed1 tr\u01b0\u1eddng \u0111\u00e3 b\u1eaft \u0111\u1ea7u \u00e1p d\u1ee5ng \u0111\u1ecbnh d\u1ea1ng m\u1edbi b\u1ed5 sung c\u00e1c c\u00e2u h\u1ecfi \u0111\u00fang\/sai v\u00e0 tr\u1ea3 l\u1eddi ng\u1eafn), c\u1ea5u tr\u00fac d\u01b0\u1edbi \u0111\u00e2y l\u00e0 m\u1eabu tham kh\u1ea3o ph\u1ed5 bi\u1ebfn nh\u1ea5t:<\/p>\n<ul style=\"padding-left: 20px;\">\n<li><strong>Ph\u1ea7n Tr\u1eafc nghi\u1ec7m (Kho\u1ea3ng 3,0 \u0111i\u1ec3m, chi\u1ebfm 30% t\u1ed5ng s\u1ed1 \u0111i\u1ec3m):<\/strong> G\u1ed3m c\u00e1c c\u00e2u h\u1ecfi kh\u00e1ch quan nhi\u1ec1u l\u1ef1a ch\u1ecdn (ho\u1eb7c k\u1ebft h\u1ee3p \u0111\u00fang\/sai), ki\u1ec3m tra nhanh kh\u1ea3 n\u0103ng n\u1eafm b\u1eaft l\u00fd thuy\u1ebft v\u1ec1 \u0111\u01a1n th\u1ee9c, \u0111a th\u1ee9c, h\u1eb1ng \u0111\u1eb3ng th\u1ee9c \u0111\u00e1ng nh\u1edb v\u00e0 c\u00e1c t\u00ednh ch\u1ea5t h\u00ecnh h\u1ecdc c\u1ee7a t\u1ee9 gi\u00e1c.<\/li>\n<li><strong>Ph\u1ea7n T\u1ef1 lu\u1eadn (Kho\u1ea3ng 7,0 \u0111i\u1ec3m, chi\u1ebfm 70% t\u1ed5ng s\u1ed1 \u0111i\u1ec3m):<\/strong> G\u1ed3m c\u00e1c b\u00e0i to\u00e1n th\u1ef1c hi\u1ec7n ph\u00e9p t\u00ednh c\u1ed9ng tr\u1eeb nh\u00e2n chia \u0111a th\u1ee9c, ph\u00e2n t\u00edch \u0111a th\u1ee9c th\u00e0nh nh\u00e2n t\u1eed, ch\u1ee9ng minh bi\u1ec3u th\u1ee9c kh\u00f4ng ph\u1ee5 thu\u1ed9c v\u00e0o bi\u1ebfn, gi\u1ea3i b\u00e0i to\u00e1n t\u00ecm x v\u00e0 c\u00e1c b\u00e0i to\u00e1n h\u00ecnh h\u1ecdc ch\u1ee9ng minh t\u00ednh ch\u1ea5t t\u1ee9 gi\u00e1c, h\u00ecnh thang c\u00e2n, h\u00ecnh b\u00ecnh h\u00e0nh, h\u00ecnh ch\u1eef nh\u1eadt, h\u00ecnh thoi, h\u00ecnh vu\u00f4ng.<\/li>\n<\/ul>\n<h3 style=\"color: #2b6cb0; font-size: 18px; margin-top: 22px;\">B\u1ea3ng ma tr\u1eadn tham kh\u1ea3o ph\u00e2n b\u1ed5 n\u1ed9i dung v\u00e0 m\u1ee9c \u0111\u1ed9 nh\u1eadn th\u1ee9c<\/h3>\n<div style=\"overflow-x: auto; margin: 15px 0;\">\n<table style=\"min-width: 640px; table-layout: fixed; font-size: 15px; width: 100%; border-collapse: collapse; border: 1px solid #cbd5e0; text-align: left;\">\n<colgroup>\n<col style=\"width: 22%;\" \/>\n<col style=\"width: 17%;\" \/>\n<col style=\"width: 17%;\" \/>\n<col style=\"width: 17%;\" \/>\n<col style=\"width: 15%;\" \/>\n<col style=\"width: 12%;\" \/><\/colgroup>\n<thead style=\"background-color: #edf2f7;\">\n<tr>\n<th style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; color: #0056b3;\">M\u1ea1ch ki\u1ebfn th\u1ee9c<\/th>\n<th style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; color: #0056b3; text-align: center;\">Nh\u1eadn bi\u1ebft<\/th>\n<th style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; color: #0056b3; text-align: center;\">Th\u00f4ng hi\u1ec3u<\/th>\n<th style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; color: #0056b3; text-align: center;\">V\u1eadn d\u1ee5ng<\/th>\n<th style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; color: #0056b3; text-align: center;\">V\u1eadn d\u1ee5ng cao<\/th>\n<th style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; color: #0056b3; text-align: center;\">T\u1ed5ng \u0111i\u1ec3m<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; font-weight: bold;\">\u0110\u01a1n th\u1ee9c, \u0111a th\u1ee9c v\u00e0 c\u00e1c ph\u00e9p t\u00ednh<\/td>\n<td style=\"white-space: nowrap; word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; text-align: center;\">1,5 \u0111i\u1ec3m<\/td>\n<td style=\"white-space: nowrap; word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; text-align: center;\">1,0 \u0111i\u1ec3m<\/td>\n<td style=\"white-space: nowrap; word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; text-align: center;\">0,5 \u0111i\u1ec3m<\/td>\n<td style=\"white-space: nowrap; word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; text-align: center;\">0 \u0111i\u1ec3m<\/td>\n<td style=\"white-space: nowrap; word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; text-align: center; font-weight: bold;\">3,0 \u0111i\u1ec3m<\/td>\n<\/tr>\n<tr>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; font-weight: bold;\">H\u1eb1ng \u0111\u1eb3ng th\u1ee9c, ph\u00e2n t\u00edch \u0111a th\u1ee9c th\u00e0nh nh\u00e2n t\u1eed<\/td>\n<td style=\"white-space: nowrap; word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; text-align: center;\">1,0 \u0111i\u1ec3m<\/td>\n<td style=\"white-space: nowrap; word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; text-align: center;\">0,75 \u0111i\u1ec3m<\/td>\n<td style=\"white-space: nowrap; word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; text-align: center;\">0,75 \u0111i\u1ec3m<\/td>\n<td style=\"white-space: nowrap; word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; text-align: center;\">0,5 \u0111i\u1ec3m<\/td>\n<td style=\"white-space: nowrap; word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; text-align: center; font-weight: bold;\">3,0 \u0111i\u1ec3m<\/td>\n<\/tr>\n<tr>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; font-weight: bold;\">T\u1ee9 gi\u00e1c v\u00e0 c\u00e1c t\u1ee9 gi\u00e1c \u0111\u1eb7c bi\u1ec7t<\/td>\n<td style=\"white-space: nowrap; word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; text-align: center;\">1,5 \u0111i\u1ec3m<\/td>\n<td style=\"white-space: nowrap; word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; text-align: center;\">1,25 \u0111i\u1ec3m<\/td>\n<td style=\"white-space: nowrap; word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; text-align: center;\">0,75 \u0111i\u1ec3m<\/td>\n<td style=\"white-space: nowrap; word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; text-align: center;\">0,5 \u0111i\u1ec3m<\/td>\n<td style=\"white-space: nowrap; word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; text-align: center; font-weight: bold;\">4,0 \u0111i\u1ec3m<\/td>\n<\/tr>\n<tr style=\"background-color: #f7fafc; font-weight: bold;\">\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; color: #0056b3;\">T\u1ed4NG \u0110I\u1ec2M (T\u1ec8 L\u1ec6 %)<\/td>\n<td style=\"white-space: nowrap; word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; text-align: center;\">4,0 \u0111i\u1ec3m (40%)<\/td>\n<td style=\"white-space: nowrap; word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; text-align: center;\">3,0 \u0111i\u1ec3m (30%)<\/td>\n<td style=\"white-space: nowrap; word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; text-align: center;\">2,0 \u0111i\u1ec3m (20%)<\/td>\n<td style=\"white-space: nowrap; word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; text-align: center;\">1,0 \u0111i\u1ec3m (10%)<\/td>\n<td style=\"white-space: nowrap; word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; text-align: center; color: #c53030;\">10,0 \u0111i\u1ec3m<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p><!-- H\u1ed8P L\u01afU \u00dd --><\/p>\n<div style=\"background-color: #edf2f7; border-left: 4px solid #0056b3; padding: 14px 18px; border-radius: 4px; margin-top: 25px;\">\n<p style=\"margin: 0; font-size: 15px; color: #2d3748;\"><strong>\ud83d\udca1 L\u01b0u \u00fd quan tr\u1ecdng cho ph\u1ee5 huynh v\u00e0 h\u1ecdc sinh:<\/strong> Ph\u1ea1m vi ki\u1ebfn th\u1ee9c v\u00e0 ph\u00e2n b\u1ed5 \u0111i\u1ec3m s\u1ed1 gi\u1eefa k\u00ec c\u00f3 th\u1ec3 c\u00f3 s\u1ef1 kh\u00e1c bi\u1ec7t nh\u1ecf t\u00f9y theo b\u1ed9 s\u00e1ch gi\u00e1o khoa (K\u1ebft n\u1ed1i tri th\u1ee9c, Ch\u00e2n tr\u1eddi s\u00e1ng t\u1ea1o ho\u1eb7c C\u00e1nh di\u1ec1u) v\u00e0 ti\u1ebfn \u0111\u1ed9 gi\u1ea3ng d\u1ea1y th\u1ef1c t\u1ebf c\u1ee7a t\u1eebng tr\u01b0\u1eddng THCS. Do \u0111\u00f3, ba m\u1eb9 n\u00ean tham kh\u1ea3o k\u1ef9 \u0111\u1ec1 c\u01b0\u01a1ng \u00f4n t\u1eadp do gi\u00e1o vi\u00ean b\u1ed9 m\u00f4n t\u1ea1i tr\u01b0\u1eddng ph\u00e1t ra \u0111\u1ec3 con \u00f4n thi \u0111\u00fang tr\u1ecdng t\u00e2m.<\/p>\n<\/div>\n<\/div>\n<p><!-- K\u1ebeT TH\u00daC: C\u1ea4U TR\u00daC \u0110\u1ec0 THI GI\u1eeeA K\u00cc 1 TO\u00c1N 8 --><\/p>\n<p><!-- B\u1eaeT \u0110\u1ea6U: PH\u1ea6N I - \u0110A TH\u1ee8C V\u00c0 H\u1eb0NG \u0110\u1eb2NG TH\u1ee8C TO\u00c1N 8 --><\/p>\n<div class=\"naviedu-content-section\" style=\"font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif; line-height: 1.8; color: #2d3748; font-size: 16px;\">\n<p><!-- BANNER PH\u1ea6N I --><\/p>\n<div style=\"background: linear-gradient(135deg, #0056b3, #0080ff); color: #ffffff; padding: 18px 24px; border-radius: 8px; margin-top: 35px; margin-bottom: 30px;\">\n<h2 id=\"muc-2-phan-i-da-thuc-va-hang-dang-thuc\" style=\"color: #ffffff; margin: 0; font-size: 22px; text-transform: uppercase; letter-spacing: 0.5px;\">Ph\u1ea7n I: \u0110a Th\u1ee9c v\u00e0 H\u1eb1ng \u0110\u1eb3ng Th\u1ee9c<\/h2>\n<\/div>\n<p><!-- CH\u1ee6 \u0110\u1ec0 1: \u0110\u01a0N TH\u1ee8C --><\/p>\n<p style=\"margin: 0 0 16px 0;\">\u0110a th\u1ee9c v\u00e0 c\u00e1c ph\u00e9p t\u00ednh l\u00e0 n\u1ec1n m\u00f3ng c\u1ee7a <strong>\u0111\u1ec1 c\u01b0\u01a1ng \u00f4n t\u1eadp gi\u1eefa k\u00ec 1 To\u00e1n 8<\/strong>. N\u1eafm ch\u1eafc c\u00e1ch thu g\u1ecdn v\u00e0 nh\u00e2n \u0111a th\u1ee9c s\u1ebd gi\u00fap con h\u1ecdc h\u1eb1ng \u0111\u1eb3ng th\u1ee9c v\u00e0 ph\u00e2n t\u00edch nh\u00e2n t\u1eed nh\u1eb9 nh\u00e0ng h\u01a1n nhi\u1ec1u.<\/p>\n<h2 id=\"muc-3-don-thuc\" style=\"color: #0056b3; border-bottom: 2px solid #e2e8f0; padding-bottom: 8px; margin-top: 35px; font-size: 20px;\">\u0110\u01a1n th\u1ee9c<\/h2>\n<h3 style=\"color: #2b6cb0; font-size: 17px; margin-top: 20px;\">Kh\u00e1i ni\u1ec7m, \u0111\u01a1n th\u1ee9c \u0111\u1ed3ng d\u1ea1ng v\u00e0 ph\u00e9p t\u00ednh c\u1ed9ng tr\u1eeb<\/h3>\n<ul style=\"padding-left: 20px;\">\n<li><strong>Kh\u00e1i ni\u1ec7m \u0111\u01a1n th\u1ee9c:<\/strong> L\u00e0 bi\u1ec3u th\u1ee9c \u0111\u1ea1i s\u1ed1 ch\u1ec9 g\u1ed3m m\u1ed9t s\u1ed1, ho\u1eb7c m\u1ed9t bi\u1ebfn, ho\u1eb7c m\u1ed9t t\u00edch gi\u1eefa c\u00e1c s\u1ed1 v\u00e0 c\u00e1c bi\u1ebfn.<\/li>\n<li><strong>\u0110\u01a1n th\u1ee9c thu g\u1ecdn:<\/strong> L\u00e0 \u0111\u01a1n th\u1ee9c ch\u1ec9 g\u1ed3m m\u1ed9t s\u1ed1 nh\u00e2n v\u1edbi c\u00e1c bi\u1ebfn, m\u00e0 m\u1ed7i bi\u1ebfn \u0111\u00e3 \u0111\u01b0\u1ee3c n\u00e2ng l\u00ean l\u0169y th\u1eeba v\u1edbi s\u1ed1 m\u0169 nguy\u00ean d\u01b0\u01a1ng v\u00e0 ch\u1ec9 xu\u1ea5t hi\u1ec7n m\u1ed9t l\u1ea7n. Ph\u1ea7n s\u1ed1 g\u1ecdi l\u00e0 h\u1ec7 s\u1ed1, ph\u1ea7n c\u00f2n l\u1ea1i g\u1ecdi l\u00e0 ph\u1ea7n bi\u1ebfn. B\u1eadc c\u1ee7a \u0111\u01a1n th\u1ee9c thu g\u1ecdn l\u00e0 t\u1ed5ng s\u1ed1 m\u0169 c\u1ee7a t\u1ea5t c\u1ea3 c\u00e1c bi\u1ebfn c\u00f3 trong \u0111\u01a1n th\u1ee9c \u0111\u00f3.<\/li>\n<li><strong>\u0110\u01a1n th\u1ee9c \u0111\u1ed3ng d\u1ea1ng:<\/strong> L\u00e0 hai \u0111\u01a1n th\u1ee9c c\u00f3 h\u1ec7 s\u1ed1 kh\u00e1c 0 v\u00e0 c\u00f3 c\u00f9ng ph\u1ea7n bi\u1ebfn.<\/li>\n<li><strong>C\u1ed9ng tr\u1eeb \u0111\u01a1n th\u1ee9c \u0111\u1ed3ng d\u1ea1ng:<\/strong> C\u1ed9ng (ho\u1eb7c tr\u1eeb) c\u00e1c h\u1ec7 s\u1ed1 v\u1edbi nhau v\u00e0 gi\u1eef nguy\u00ean ph\u1ea7n bi\u1ebfn.<\/li>\n<\/ul>\n<p><!-- H\u1ed8P L\u1ed6I SAI TH\u01af\u1edcNG G\u1eb6P --><\/p>\n<div style=\"background-color: #fff5f5; border-left: 4px solid #e53e3e; padding: 14px 18px; border-radius: 4px; margin: 18px 0;\">\n<p style=\"margin: 0 0 6px 0; font-weight: bold; color: #c53030;\">\u26a0\ufe0f L\u1ed7i sai th\u01b0\u1eddng g\u1eb7p v\u1ec1 b\u1eadc c\u1ee7a \u0111\u01a1n th\u1ee9c:<\/p>\n<ul style=\"margin: 0; padding-left: 20px; font-size: 15px;\">\n<li>Nh\u1ea7m l\u1eabn t\u00ednh b\u1eadc c\u1ee7a \u0111\u01a1n th\u1ee9c ch\u01b0a thu g\u1ecdn (c\u1ed9ng qu\u00ean s\u1ed1 m\u0169 ho\u1eb7c t\u00ednh nh\u1ea7m s\u1ed1 m\u0169 c\u1ee7a h\u1eb1ng s\u1ed1) ho\u1eb7c c\u1ed9ng tr\u1eeb c\u00e1c \u0111\u01a1n th\u1ee9c kh\u00f4ng \u0111\u1ed3ng d\u1ea1ng.<\/li>\n<\/ul>\n<\/div>\n<p><!-- V\u00cd D\u1ee4 M\u1eaaU --><\/p>\n<div style=\"background-color: #f7fafc; border-left: 4px solid #0056b3; padding: 16px 20px; border-radius: 4px; margin: 18px 0;\">\n<p style=\"font-weight: bold; color: #0056b3; margin: 0 0 8px 0;\">V\u00ed d\u1ee5 m\u1eabu gi\u1ea3i chi ti\u1ebft: Thu g\u1ecdn v\u00e0 t\u00ednh b\u1eadc \u0111\u01a1n th\u1ee9c<\/p>\n<p style=\"margin: 0 0 6px 0;\"><strong>\u0110\u1ec1 b\u00e0i:<\/strong> Thu g\u1ecdn \u0111\u01a1n th\u1ee9c sau v\u00e0 t\u00ecm h\u1ec7 s\u1ed1, ph\u1ea7n bi\u1ebfn, b\u1eadc c\u1ee7a n\u00f3: <code>A = 3 \u00b7 x<sup>2<\/sup> \u00b7 y \u00b7 (-2) \u00b7 x \u00b7 y<sup>3<\/sup><\/code>.<\/p>\n<p style=\"margin: 0;\"><strong>L\u1eddi gi\u1ea3i chi ti\u1ebft:<\/strong><br \/>\n\u2022 Nh\u00f3m c\u00e1c h\u1ec7 s\u1ed1 v\u1edbi nhau v\u00e0 c\u00e1c bi\u1ebfn c\u00f9ng t\u00ean v\u1edbi nhau theo t\u00ednh ch\u1ea5t giao ho\u00e1n v\u00e0 k\u1ebft h\u1ee3p:<br \/>\n<code>A = [3 \u00b7 (-2)] \u00b7 (x<sup>2<\/sup> \u00b7 x) \u00b7 (y \u00b7 y<sup>3<\/sup>)<\/code><br \/>\n\u2022 Th\u1ef1c hi\u1ec7n ph\u00e9p t\u00ednh nh\u00e2n c\u00e1c h\u1ec7 s\u1ed1 v\u00e0 c\u1ed9ng s\u1ed1 m\u0169 c\u00e1c bi\u1ebfn c\u00f9ng c\u01a1 s\u1edf:<br \/>\n<code>A = -6 \u00b7 x<sup>3<\/sup> \u00b7 y<sup>4<\/sup><\/code>.<br \/>\n\u2022 X\u00e1c \u0111\u1ecbnh c\u00e1c th\u00e0nh ph\u1ea7n:<br \/>\n&#8211; H\u1ec7 s\u1ed1:<\/p>\n<p style=\"margin: 0;\"><code>-6<\/code>.<br \/>\n&#8211; Ph\u1ea7n bi\u1ebfn: <code>x<sup>3<\/sup>y<sup>4<\/sup><\/code>.<br \/>\n&#8211; B\u1eadc c\u1ee7a \u0111\u01a1n th\u1ee9c: <code>3 + 4 = 7<\/code>.<br \/>\n\u2022 <strong>\u0110\u00e1p s\u1ed1:<\/strong> \u0110\u01a1n th\u1ee9c thu g\u1ecdn l\u00e0 <code>-6x<sup>3<\/sup>y<sup>4<\/sup><\/code>, h\u1ec7 s\u1ed1 l\u00e0 -6, ph\u1ea7n bi\u1ebfn l\u00e0 x<sup>3<\/sup>y<sup>4<\/sup>, b\u1eadc b\u1eb1ng 7.<\/p>\n<\/div>\n<p><!-- CH\u1ee6 \u0110\u1ec0 2: \u0110A TH\u1ee8C NHI\u1ec0U BI\u1ebeN --><\/p>\n<h2 id=\"muc-4-da-thuc-nhieu-bien\" style=\"color: #0056b3; border-bottom: 2px solid #e2e8f0; padding-bottom: 8px; margin-top: 35px; font-size: 20px;\">\u0110a th\u1ee9c nhi\u1ec1u bi\u1ebfn<\/h2>\n<h3 style=\"color: #2b6cb0; font-size: 17px; margin-top: 20px;\">Kh\u00e1i ni\u1ec7m, thu g\u1ecdn \u0111a th\u1ee9c v\u00e0 t\u00ednh gi\u00e1 tr\u1ecb<\/h3>\n<ul style=\"padding-left: 20px;\">\n<li><strong>Kh\u00e1i ni\u1ec7m \u0111a th\u1ee9c:<\/strong> L\u00e0 m\u1ed9t t\u1ed5ng c\u1ee7a nh\u1eefng \u0111\u01a1n th\u1ee9c. M\u1ed7i \u0111\u01a1n th\u1ee9c trong t\u1ed5ng g\u1ecdi l\u00e0 m\u1ed9t h\u1ea1ng t\u1eed c\u1ee7a \u0111a th\u1ee9c \u0111\u00f3.<\/li>\n<li><strong>\u0110a th\u1ee9c thu g\u1ecdn:<\/strong> L\u00e0 \u0111a th\u1ee9c kh\u00f4ng c\u00f2n hai h\u1ea1ng t\u1eed n\u00e0o \u0111\u1ed3ng d\u1ea1ng.<\/li>\n<li><strong>B\u1eadc c\u1ee7a \u0111a th\u1ee9c:<\/strong> L\u00e0 b\u1eadc c\u1ee7a h\u1ea1ng t\u1eed c\u00f3 b\u1eadc cao nh\u1ea5t trong d\u1ea1ng thu g\u1ecdn c\u1ee7a \u0111a th\u1ee9c \u0111\u00f3.<\/li>\n<li><strong>T\u00ednh gi\u00e1 tr\u1ecb c\u1ee7a \u0111a th\u1ee9c:<\/strong> Thay c\u00e1c gi\u00e1 tr\u1ecb cho tr\u01b0\u1edbc c\u1ee7a bi\u1ebfn v\u00e0o \u0111a th\u1ee9c r\u1ed3i th\u1ef1c hi\u1ec7n c\u00e1c ph\u00e9p t\u00ednh s\u1ed1 h\u1ecdc.<\/li>\n<\/ul>\n<p><!-- H\u1ed8P L\u1ed6I SAI TH\u01af\u1edcNG G\u1eb6P --><\/p>\n<div style=\"background-color: #fff5f5; border-left: 4px solid #e53e3e; padding: 14px 18px; border-radius: 4px; margin: 18px 0;\">\n<p style=\"margin: 0 0 6px 0; font-weight: bold; color: #c53030;\">\u26a0\ufe0f L\u1ed7i sai th\u01b0\u1eddng g\u1eb7p khi x\u00e1c \u0111\u1ecbnh b\u1eadc \u0111a th\u1ee9c:<\/p>\n<ul style=\"margin: 0; padding-left: 20px; font-size: 15px;\">\n<li>L\u1ea5y t\u1ed5ng b\u1eadc c\u1ee7a t\u1ea5t c\u1ea3 c\u00e1c h\u1ea1ng t\u1eed trong \u0111a th\u1ee9c c\u1ed9ng l\u1ea1i v\u1edbi nhau thay v\u00ec ch\u1ec9 ch\u1ecdn b\u1eadc c\u1ee7a h\u1ea1ng t\u1eed cao nh\u1ea5t sau khi \u0111\u00e3 thu g\u1ecdn \u0111a th\u1ee9c.<\/li>\n<\/ul>\n<\/div>\n<p><!-- V\u00cd D\u1ee4 M\u1eaaU --><\/p>\n<div style=\"background-color: #f7fafc; border-left: 4px solid #0056b3; padding: 16px 20px; border-radius: 4px; margin: 18px 0;\">\n<p style=\"font-weight: bold; color: #0056b3; margin: 0 0 8px 0;\">V\u00ed d\u1ee5 m\u1eabu gi\u1ea3i chi ti\u1ebft: Thu g\u1ecdn \u0111a th\u1ee9c v\u00e0 t\u00ednh gi\u00e1 tr\u1ecb<\/p>\n<p style=\"margin: 0 0 6px 0;\"><strong>\u0110\u1ec1 b\u00e0i:<\/strong> Thu g\u1ecdn \u0111a th\u1ee9c sau v\u00e0 t\u00ednh gi\u00e1 tr\u1ecb c\u1ee7a n\u00f3 t\u1ea1i x = 1, y = -2:<br \/>\n<code>P = 2x<sup>2<\/sup>y - 3xy + 5x<sup>2<\/sup>y + 3xy - 7x<sup>2<\/sup><\/code>.<\/p>\n<p style=\"margin: 0;\"><strong>L\u1eddi gi\u1ea3i chi ti\u1ebft:<\/strong><br \/>\n\u2022 Nh\u00f3m c\u00e1c h\u1ea1ng t\u1eed \u0111\u1ed3ng d\u1ea1ng v\u1edbi nhau:<br \/>\n<code>P = (2x<sup>2<\/sup>y + 5x<sup>2<\/sup>y) + (-3xy + 3xy) - 7x<sup>2<\/sup><\/code><br \/>\n\u2022 Thu g\u1ecdn c\u00e1c nh\u00f3m h\u1ea1ng t\u1eed:<br \/>\n<code>P = 7x<sup>2<\/sup>y - 7x<sup>2<\/sup><\/code>.<br \/>\n\u2022 Thay x = 1 v\u00e0 y = -2 v\u00e0o \u0111a th\u1ee9c \u0111\u00e3 thu g\u1ecdn:<\/p>\n<p style=\"margin: 0;\"><code>P = 7 \u00b7 (1)<sup>2<\/sup> \u00b7 (-2) - 7 \u00b7 (1)<sup>2<\/sup> = 7 \u00b7 1 \u00b7 (-2) - 7 \u00b7 1 = -14 - 7 = -21<\/code>.<br \/>\n\u2022 <strong>\u0110\u00e1p s\u1ed1:<\/strong> \u0110a th\u1ee9c thu g\u1ecdn l\u00e0 <code>7x<sup>2<\/sup>y - 7x<sup>2<\/sup><\/code> v\u00e0 gi\u00e1 tr\u1ecb t\u1ea1i x = 1, y = -2 b\u1eb1ng <code>-21<\/code>.<\/p>\n<\/div>\n<p><!-- CH\u1ee6 \u0110\u1ec0 3: C\u1ed8NG, TR\u1eea, NH\u00c2N \u0110A TH\u1ee8C --><\/p>\n<h2 id=\"muc-5-cong-tru-nhan-da-thuc\" style=\"color: #0056b3; border-bottom: 2px solid #e2e8f0; padding-bottom: 8px; margin-top: 35px; font-size: 20px;\">C\u1ed9ng, tr\u1eeb, nh\u00e2n \u0111a th\u1ee9c<\/h2>\n<h3 style=\"color: #2b6cb0; font-size: 17px; margin-top: 20px;\">C\u00e1c quy t\u1eafc ph\u00e9p t\u00ednh \u0111\u1ea1i s\u1ed1 \u0111a th\u1ee9c<\/h3>\n<ul style=\"padding-left: 20px;\">\n<li><strong>C\u1ed9ng, tr\u1eeb \u0111a th\u1ee9c:<\/strong> Th\u1ef1c hi\u1ec7n quy t\u1eafc b\u1ecf ngo\u1eb7c (ch\u00fa \u00fd \u0111\u1ed5i d\u1ea5u khi tr\u01b0\u1edbc ngo\u1eb7c c\u00f3 d\u1ea5u tr\u1eeb), sau \u0111\u00f3 nh\u00f3m c\u00e1c h\u1ea1ng t\u1eed \u0111\u1ed3ng d\u1ea1ng v\u00e0 c\u1ed9ng tr\u1eeb ch\u00fang.<\/li>\n<li><strong>Nh\u00e2n \u0111\u01a1n th\u1ee9c v\u1edbi \u0111a th\u1ee9c:<\/strong> Nh\u00e2n \u0111\u01a1n th\u1ee9c \u0111\u00f3 v\u1edbi t\u1eebng h\u1ea1ng t\u1eed c\u1ee7a \u0111a th\u1ee9c r\u1ed3i c\u1ed9ng c\u00e1c t\u00edch l\u1ea1i v\u1edbi nhau: <code>A \u00b7 (B + C) = A \u00b7 B + A \u00b7 C<\/code>.<\/li>\n<li><strong>Nh\u00e2n \u0111a th\u1ee9c v\u1edbi \u0111a th\u1ee9c:<\/strong> Nh\u00e2n t\u1eebng h\u1ea1ng t\u1eed c\u1ee7a \u0111a th\u1ee9c n\u00e0y v\u1edbi t\u1eebng h\u1ea1ng t\u1eed c\u1ee7a \u0111a th\u1ee9c kia r\u1ed3i c\u1ed9ng t\u1ea5t c\u1ea3 c\u00e1c t\u00edch l\u1ea1i v\u1edbi nhau: <code>(A + B) \u00b7 (C + D) = A \u00b7 C + A \u00b7 D + B \u00b7 C + B \u00b7 D<\/code>.<\/li>\n<\/ul>\n<p><!-- H\u1ed8P L\u1ed6I SAI TH\u01af\u1edcNG G\u1eb6P --><\/p>\n<div style=\"background-color: #fff5f5; border-left: 4px solid #e53e3e; padding: 14px 18px; border-radius: 4px; margin: 18px 0;\">\n<p style=\"margin: 0 0 6px 0; font-weight: bold; color: #c53030;\">\u26a0\ufe0f L\u1ed7i sai th\u01b0\u1eddng g\u1eb7p khi nh\u00e2n \u0111a th\u1ee9c:<\/p>\n<ul style=\"margin: 0; padding-left: 20px; font-size: 15px;\">\n<li>B\u1ecf qu\u00ean d\u1ea5u tr\u1eeb khi ph\u00e1 ngo\u1eb7c tr\u01b0\u1edbc m\u1ed9t \u0111a th\u1ee9c ho\u1eb7c nh\u00e2n thi\u1ebfu h\u1ea1ng t\u1eed khi th\u1ef1c hi\u1ec7n ph\u00e9p nh\u00e2n hai \u0111a th\u1ee9c nhi\u1ec1u bi\u1ebfn.<\/li>\n<\/ul>\n<\/div>\n<p><!-- V\u00cd D\u1ee4 M\u1eaaU --><\/p>\n<div style=\"background-color: #f7fafc; border-left: 4px solid #0056b3; padding: 16px 20px; border-radius: 4px; margin: 18px 0;\">\n<p style=\"font-weight: bold; color: #0056b3; margin: 0 0 8px 0;\">V\u00ed d\u1ee5 m\u1eabu gi\u1ea3i chi ti\u1ebft: Th\u1ef1c hi\u1ec7n ph\u00e9p nh\u00e2n \u0111a th\u1ee9c<\/p>\n<p style=\"margin: 0 0 6px 0;\"><strong>\u0110\u1ec1 b\u00e0i:<\/strong> Khai tri\u1ec3n v\u00e0 thu g\u1ecdn bi\u1ec3u th\u1ee9c sau: <code>Q = (2x - 3) \u00b7 (x<sup>2<\/sup> - 4x + 1)<\/code>.<\/p>\n<p style=\"margin: 0;\"><strong>L\u1eddi gi\u1ea3i chi ti\u1ebft:<\/strong><br \/>\n\u2022 Nh\u00e2n t\u1eebng h\u1ea1ng t\u1eed c\u1ee7a \u0111a th\u1ee9c th\u1ee9 nh\u1ea5t v\u1edbi \u0111a th\u1ee9c th\u1ee9 hai:<br \/>\n<code>Q = 2x \u00b7 (x<sup>2<\/sup> - 4x + 1) - 3 \u00b7 (x<sup>2<\/sup> - 4x + 1)<\/code><br \/>\n\u2022 Ph\u00e2n ph\u1ed1i \u0111\u01a1n th\u1ee9c v\u00e0o trong ngo\u1eb7c:<br \/>\n<code>Q = (2x<sup>3<\/sup> - 8x<sup>2<\/sup> + 2x) - (3x<sup>2<\/sup> - 12x + 3)<\/code><br \/>\n\u2022 Ph\u00e1 ngo\u1eb7c v\u00e0 \u0111\u1ed5i d\u1ea5u ch\u00ednh x\u00e1c:<\/p>\n<p style=\"margin: 0;\"><code>Q = 2x<sup>3<\/sup> - 8x<sup>2<\/sup> + 2x - 3x<sup>2<\/sup> + 12x - 3<\/code><br \/>\n\u2022 Nh\u00f3m c\u00e1c h\u1ea1ng t\u1eed \u0111\u1ed3ng d\u1ea1ng:<br \/>\n<code>Q = 2x<sup>3<\/sup> + (-8x<sup>2<\/sup> - 3x<sup>2<\/sup>) + (2x + 12x) - 3<\/code><br \/>\n<code>Q = 2x<sup>3<\/sup> - 11x<sup>2<\/sup> + 14x - 3<\/code>.<br \/>\n\u2022 <strong>\u0110\u00e1p s\u1ed1:<\/strong> Bi\u1ec3u th\u1ee9c sau khi khai tri\u1ec3n l\u00e0 <code>2x<sup>3<\/sup> - 11x<sup>2<\/sup> + 14x - 3<\/code>.<\/p>\n<\/div>\n<p><!-- CH\u1ee6 \u0110\u1ec0 4: CHIA \u0110A TH\u1ee8C CHO \u0110\u01a0N TH\u1ee8C --><\/p>\n<h2 id=\"muc-6-chia-da-thuc-cho-don-thuc\" style=\"color: #0056b3; border-bottom: 2px solid #e2e8f0; padding-bottom: 8px; margin-top: 35px; font-size: 20px;\">Chia \u0111a th\u1ee9c cho \u0111\u01a1n th\u1ee9c<\/h2>\n<h3 style=\"color: #2b6cb0; font-size: 17px; margin-top: 20px;\">\u0110i\u1ec1u ki\u1ec7n chia h\u1ebft v\u00e0 quy t\u1eafc chia<\/h3>\n<ul style=\"padding-left: 20px;\">\n<li><strong>\u0110i\u1ec1u ki\u1ec7n chia h\u1ebft:<\/strong> M\u1ed9t \u0111a th\u1ee9c chia h\u1ebft cho m\u1ed9t \u0111\u01a1n th\u1ee9c n\u1ebfu m\u1ecdi h\u1ea1ng t\u1eed c\u1ee7a \u0111a th\u1ee9c \u0111\u00f3 \u0111\u1ec1u chia h\u1ebft cho \u0111\u01a1n th\u1ee9c chia (t\u1ee9c l\u00e0 m\u1ed7i bi\u1ebfn c\u1ee7a \u0111\u01a1n th\u1ee9c chia \u0111\u1ec1u c\u00f3 m\u1eb7t trong t\u1eebng h\u1ea1ng t\u1eed c\u1ee7a \u0111a th\u1ee9c v\u1edbi s\u1ed1 m\u0169 kh\u00f4ng nh\u1ecf h\u01a1n s\u1ed1 m\u0169 c\u1ee7a n\u00f3 trong \u0111\u01a1n th\u1ee9c chia).<\/li>\n<li><strong>Quy t\u1eafc chia \u0111a th\u1ee9c cho \u0111\u01a1n th\u1ee9c:<\/strong> Mu\u1ed1n chia \u0111a th\u1ee9c A cho \u0111\u01a1n th\u1ee9c B (v\u1edbi B kh\u00e1c 0), ta chia t\u1eebng h\u1ea1ng t\u1eed c\u1ee7a \u0111a th\u1ee9c A cho \u0111\u01a1n th\u1ee9c B r\u1ed3i c\u1ed9ng c\u00e1c k\u1ebft qu\u1ea3 l\u1ea1i v\u1edbi nhau: <code>(A + B - C) : D = (A : D) + (B : D) - (C : D)<\/code>.<\/li>\n<\/ul>\n<p><!-- H\u1ed8P L\u1ed6I SAI TH\u01af\u1edcNG G\u1eb6P --><\/p>\n<div style=\"background-color: #fff5f5; border-left: 4px solid #e53e3e; padding: 14px 18px; border-radius: 4px; margin: 18px 0;\">\n<p style=\"margin: 0 0 6px 0; font-weight: bold; color: #c53030;\">\u26a0\ufe0f L\u1ed7i sai th\u01b0\u1eddng g\u1eb7p khi chia \u0111a th\u1ee9c:<\/p>\n<ul style=\"margin: 0; padding-left: 20px; font-size: 15px;\">\n<li>Qu\u00ean chia m\u1ed9t h\u1ea1ng t\u1eed b\u1ea5t k\u00ec trong \u0111a th\u1ee9c cho \u0111\u01a1n th\u1ee9c ho\u1eb7c tr\u1eeb nh\u1ea7m s\u1ed1 m\u0169 c\u1ee7a bi\u1ebfn khi \u00e1p d\u1ee5ng c\u00f4ng th\u1ee9c chia hai l\u0169y th\u1eeba c\u00f9ng c\u01a1 s\u1edf.<\/li>\n<\/ul>\n<\/div>\n<p><!-- V\u00cd D\u1ee4 M\u1eaaU --><\/p>\n<div style=\"background-color: #f7fafc; border-left: 4px solid #0056b3; padding: 16px 20px; border-radius: 4px; margin: 18px 0;\">\n<p style=\"font-weight: bold; color: #0056b3; margin: 0 0 8px 0;\">V\u00ed d\u1ee5 m\u1eabu gi\u1ea3i chi ti\u1ebft: Th\u1ef1c hi\u1ec7n ph\u00e9p chia \u0111a th\u1ee9c cho \u0111\u01a1n th\u1ee9c<\/p>\n<p style=\"margin: 0 0 6px 0;\"><strong>\u0110\u1ec1 b\u00e0i:<\/strong> Th\u1ef1c hi\u1ec7n ph\u00e9p t\u00ednh chia \u0111a th\u1ee9c: <code>(6x<sup>4<\/sup>y<sup>3<\/sup> - 9x<sup>3<\/sup>y<sup>2<\/sup> + 3x<sup>2<\/sup>y) : (3x<sup>2<\/sup>y)<\/code>.<\/p>\n<p style=\"margin: 0;\"><strong>L\u1eddi gi\u1ea3i chi ti\u1ebft:<\/strong><br \/>\n\u2022 Chia t\u1eebng h\u1ea1ng t\u1eed c\u1ee7a \u0111a th\u1ee9c cho \u0111\u01a1n th\u1ee9c <code>3x<sup>2<\/sup>y<\/code>:<br \/>\n<code>= (6x<sup>4<\/sup>y<sup>3<\/sup> : 3x<sup>2<\/sup>y) + (-9x<sup>3<\/sup>y<sup>2<\/sup> : 3x<sup>2<\/sup>y) + (3x<sup>2<\/sup>y : 3x<sup>2<\/sup>y)<\/code><br \/>\n\u2022 Th\u1ef1c hi\u1ec7n ph\u00e9p chia t\u1eebng h\u1ec7 s\u1ed1 v\u00e0 tr\u1eeb s\u1ed1 m\u0169 c\u00e1c bi\u1ebfn t\u01b0\u01a1ng \u1ee9ng:<br \/>\n&#8211; H\u1ea1ng t\u1eed th\u1ee9 nh\u1ea5t: <code>(6 : 3) \u00b7 (x<sup>4<\/sup> : x<sup>2<\/sup>) \u00b7 (y<sup>3<\/sup> : y) = 2x<sup>2<\/sup>y<sup>2<\/sup><\/code>.<br \/>\n&#8211; H\u1ea1ng t\u1eed th\u1ee9 hai:<\/p>\n<p style=\"margin: 0;\"><code>(-9 : 3) \u00b7 (x<sup>3<\/sup> : x<sup>2<\/sup>) \u00b7 (y<sup>2<\/sup> : y) = -3xy<\/code>.<br \/>\n&#8211; H\u1ea1ng t\u1eed th\u1ee9 ba: <code>(3 : 3) \u00b7 (x<sup>2<\/sup> : x<sup>2<\/sup>) \u00b7 (y : y) = 1<\/code>.<br \/>\n\u2022 T\u1ed5ng h\u1ee3p k\u1ebft qu\u1ea3:<br \/>\n<code>= 2x<sup>2<\/sup>y<sup>2<\/sup> - 3xy + 1<\/code>.<br \/>\n\u2022 <strong>\u0110\u00e1p s\u1ed1:<\/strong> K\u1ebft qu\u1ea3 ph\u00e9p chia l\u00e0 <code>2x<sup>2<\/sup>y<sup>2<\/sup> - 3xy + 1<\/code>.<\/p>\n<\/div>\n<\/div>\n<p><!-- K\u1ebeT TH\u00daC: PH\u1ea6N I - \u0110A TH\u1ee8C V\u00c0 H\u1eb0NG \u0110\u1eb2NG TH\u1ee8C TO\u00c1N 8 --><\/p>\n<p><!-- B\u1eaeT \u0110\u1ea6U: PH\u1ea6N I (TI\u1ebeP THEO) - H\u1eb0NG \u0110\u1eb2NG TH\u1ee8C V\u00c0 PH\u00c2N T\u00cdCH \u0110A TH\u1ee8C TO\u00c1N 8 --><\/p>\n<div class=\"naviedu-content-section\" style=\"font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif; line-height: 1.8; color: #2d3748; font-size: 16px;\">\n<p><!-- CH\u1ee6 \u0110\u1ec0 5: H\u1eb0NG \u0110\u1eb2NG TH\u1ee8C \u0110\u00c1NG NH\u1eda --><\/p>\n<p style=\"margin: 0 0 16px 0;\">H\u1eb1ng \u0111\u1eb3ng th\u1ee9c v\u00e0 ph\u00e2n t\u00edch \u0111a th\u1ee9c th\u00e0nh nh\u00e2n t\u1eed l\u00e0 nh\u00f3m b\u00e0i tr\u1ecdng t\u00e2m nh\u1ea5t c\u1ee7a \u0111\u1ec1 c\u01b0\u01a1ng \u00f4n t\u1eadp gi\u1eefa k\u00ec 1 To\u00e1n 8, c\u0169ng l\u00e0 ki\u1ebfn th\u1ee9c s\u1ebd theo con \u0111\u1ebfn k\u00ec thi v\u00e0o 10.<\/p>\n<h2 id=\"muc-7-hang-dang-thuc-dang-nho\" style=\"color: #0056b3; border-bottom: 2px solid #e2e8f0; padding-bottom: 8px; margin-top: 35px; font-size: 20px;\">H\u1eb1ng \u0111\u1eb3ng th\u1ee9c \u0111\u00e1ng nh\u1edb<\/h2>\n<h3 style=\"color: #2b6cb0; font-size: 17px; margin-top: 20px;\">B\u1ea3y h\u1eb1ng \u0111\u1eb3ng th\u1ee9c \u0111\u00e1ng nh\u1edb v\u00e0 \u1ee9ng d\u1ee5ng t\u00ednh nhanh<\/h3>\n<p>H\u1eb1ng \u0111\u1eb3ng th\u1ee9c \u0111\u00e1ng nh\u1edb l\u00e0 c\u00f4ng c\u1ee5 c\u1ed1t l\u00f5i trong ch\u01b0\u01a1ng tr\u00ecnh \u0110\u1ea1i s\u1ed1 l\u1edbp 8, gi\u00fap h\u1ecdc sinh khai tri\u1ec3n bi\u1ec3u th\u1ee9c, ph\u00e2n t\u00edch nh\u00e2n t\u1eed v\u00e0 t\u00ednh nhanh m\u1ed9t c\u00e1ch t\u1ed1i \u01b0u. D\u01b0\u1edbi \u0111\u00e2y l\u00e0 b\u1ea3ng t\u1ed5ng h\u1ee3p 7 h\u1eb1ng \u0111\u1eb3ng th\u1ee9c c\u01a1 b\u1ea3n:<\/p>\n<p><!-- B\u1ea2NG 7 H\u1eb0NG \u0110\u1eb2NG TH\u1ee8C \u0110\u00c1NG NH\u1eda --><\/p>\n<div style=\"overflow-x: auto; margin: 15px 0;\">\n<table style=\"table-layout: auto; font-size: 14px; width: 100%; border-collapse: collapse; border: 1px solid #cbd5e0; text-align: left;\">\n<thead style=\"background-color: #edf2f7;\">\n<tr>\n<th style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; color: #0056b3; width: 45%;\">T\u00ean g\u1ecdi h\u1eb1ng \u0111\u1eb3ng th\u1ee9c<\/th>\n<th style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; color: #0056b3; width: 55%;\">C\u00f4ng th\u1ee9c t\u1ed5ng qu\u00e1t<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; font-weight: bold;\">1. B\u00ecnh ph\u01b0\u01a1ng c\u1ee7a m\u1ed9t t\u1ed5ng<\/td>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; font-family: monospace; color: #2b6cb0;\">(A + B)<sup>2<\/sup> = A<sup>2<\/sup> + 2AB + B<sup>2<\/sup><\/td>\n<\/tr>\n<tr>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; font-weight: bold;\">2. B\u00ecnh ph\u01b0\u01a1ng c\u1ee7a m\u1ed9t hi\u1ec7u<\/td>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; font-family: monospace; color: #2b6cb0;\">(A &#8211; B)<sup>2<\/sup> = A<sup>2<\/sup> &#8211; 2AB + B<sup>2<\/sup><\/td>\n<\/tr>\n<tr>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; font-weight: bold;\">3. Hi\u1ec7u hai b\u00ecnh ph\u01b0\u01a1ng<\/td>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; font-family: monospace; color: #2b6cb0;\">A<sup>2<\/sup> &#8211; B<sup>2<\/sup> = (A &#8211; B)(A + B)<\/td>\n<\/tr>\n<tr>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; font-weight: bold;\">4. L\u1eadp ph\u01b0\u01a1ng c\u1ee7a m\u1ed9t t\u1ed5ng<\/td>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; font-family: monospace; color: #2b6cb0;\">(A + B)<sup>3<\/sup> = A<sup>3<\/sup> + 3A<sup>2<\/sup>B + 3AB<sup>2<\/sup> + B<sup>3<\/sup><\/td>\n<\/tr>\n<tr>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; font-weight: bold;\">5. L\u1eadp ph\u01b0\u01a1ng c\u1ee7a m\u1ed9t hi\u1ec7u<\/td>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; font-family: monospace; color: #2b6cb0;\">(A &#8211; B)<sup>3<\/sup> = A<sup>3<\/sup> &#8211; 3A<sup>2<\/sup>B + 3AB<sup>2<\/sup> &#8211; B<sup>3<\/sup><\/td>\n<\/tr>\n<tr>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; font-weight: bold;\">6. T\u1ed5ng hai l\u1eadp ph\u01b0\u01a1ng<\/td>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; font-family: monospace; color: #2b6cb0;\">A<sup>3<\/sup> + B<sup>3<\/sup> = (A + B)(A<sup>2<\/sup> &#8211; AB + B<sup>2<\/sup>)<\/td>\n<\/tr>\n<tr>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; font-weight: bold;\">7. Hi\u1ec7u hai l\u1eadp ph\u01b0\u01a1ng<\/td>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; font-family: monospace; color: #2b6cb0;\">A<sup>3<\/sup> &#8211; B<sup>3<\/sup> = (A &#8211; B)(A<sup>2<\/sup> + AB + B<sup>2<\/sup>)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p><!-- H\u1ed8P L\u1ed6I SAI TH\u01af\u1edcNG G\u1eb6P --><\/p>\n<div style=\"background-color: #fff5f5; border-left: 4px solid #e53e3e; padding: 14px 18px; border-radius: 4px; margin: 18px 0;\">\n<p style=\"margin: 0 0 6px 0; font-weight: bold; color: #c53030;\">\u26a0\ufe0f L\u1ed7i sai th\u01b0\u1eddng g\u1eb7p khi d\u00f9ng h\u1eb1ng \u0111\u1eb3ng th\u1ee9c:<\/p>\n<ul style=\"margin: 0; padding-left: 20px; font-size: 15px;\">\n<li>Qu\u00ean h\u1ec7 s\u1ed1 2 trong s\u1ed1 h\u1ea1ng 2AB c\u1ee7a h\u1eb1ng \u0111\u1eb3ng th\u1ee9c b\u00ecnh ph\u01b0\u01a1ng, ho\u1eb7c nh\u1ea7m d\u1ea5u \u1edf h\u1eb1ng \u0111\u1eb3ng th\u1ee9c hi\u1ec7u hai l\u1eadp ph\u01b0\u01a1ng v\u00e0 t\u1ed5ng hai l\u1eadp ph\u01b0\u01a1ng (vi\u1ebft nh\u1ea7m d\u1ea5u c\u1ed9ng th\u00e0nh d\u1ea5u tr\u1eeb \u1edf t\u00edch kh\u00f4ng \u0111\u1ea7y \u0111\u1ee7).<\/li>\n<\/ul>\n<\/div>\n<p><!-- V\u00cd D\u1ee4 M\u1eaaU --><\/p>\n<div style=\"background-color: #f7fafc; border-left: 4px solid #0056b3; padding: 16px 20px; border-radius: 4px; margin: 18px 0;\">\n<p style=\"font-weight: bold; color: #0056b3; margin: 0 0 8px 0;\">V\u00ed d\u1ee5 m\u1eabu gi\u1ea3i chi ti\u1ebft: T\u00ednh nhanh gi\u00e1 tr\u1ecb bi\u1ec3u th\u1ee9c<\/p>\n<p style=\"margin: 0 0 6px 0;\"><strong>\u0110\u1ec1 b\u00e0i:<\/strong> T\u00ednh nhanh gi\u00e1 tr\u1ecb c\u00e1c bi\u1ec3u th\u1ee9c sau b\u1eb1ng c\u00e1ch \u00e1p d\u1ee5ng h\u1eb1ng \u0111\u1eb3ng th\u1ee9c:<br \/>\na) A = 99<sup>2<\/sup><br \/>\nb) B = 101 \u00b7 99<\/p>\n<p style=\"margin: 0;\"><strong>L\u1eddi gi\u1ea3i chi ti\u1ebft:<\/strong><br \/>\n\u2022 X\u00e9t \u00fd a:<br \/>\n&#8211; Bi\u1ebfn \u0111\u1ed5i 99 th\u00e0nh <code>(100 - 1)<\/code>.<br \/>\n&#8211; \u00c1p d\u1ee5ng h\u1eb1ng \u0111\u1eb3ng th\u1ee9c b\u00ecnh ph\u01b0\u01a1ng c\u1ee7a m\u1ed9t hi\u1ec7u: <code>99<sup>2<\/sup> = (100 - 1)<sup>2<\/sup> = 100<sup>2<\/sup> - 2 \u00b7 100 \u00b7 1 + 1<sup>2<\/sup><\/code>.<br \/>\n&#8211; T\u00ednh to\u00e1n:<\/p>\n<p style=\"margin: 0;\"><code>10000 - 200 + 1 = 9801<\/code>.<br \/>\n\u2022 X\u00e9t \u00fd b:<br \/>\n&#8211; Bi\u1ebft 101 = 100 + 1 v\u00e0 99 = 100 &#8211; 1.<br \/>\n&#8211; \u00c1p d\u1ee5ng h\u1eb1ng \u0111\u1eb3ng th\u1ee9c hi\u1ec7u hai b\u00ecnh ph\u01b0\u01a1ng: <code>101 \u00b7 99 = (100 + 1)(100 - 1) = 100<sup>2<\/sup> - 1<sup>2<\/sup><\/code>.<br \/>\n&#8211; T\u00ednh to\u00e1n: <code>10000 - 1 = 9999<\/code>.<br \/>\n\u2022 <strong>\u0110\u00e1p s\u1ed1:<\/strong> a) A = 9801 ; b) B = 9999.<\/p>\n<\/div>\n<p><!-- CH\u1ee6 \u0110\u1ec0 6: PH\u00c2N T\u00cdCH \u0110A TH\u1ee8C TH\u00c0NH NH\u00c2N T\u1eec --><\/p>\n<h2 id=\"muc-8-phan-tich-da-thuc-thanh-nhan-tu\" style=\"color: #0056b3; border-bottom: 2px solid #e2e8f0; padding-bottom: 8px; margin-top: 35px; font-size: 20px;\">Ph\u00e2n t\u00edch \u0111a th\u1ee9c th\u00e0nh nh\u00e2n t\u1eed<\/h2>\n<h3 style=\"color: #2b6cb0; font-size: 17px; margin-top: 20px;\">B\u1ed1n ph\u01b0\u01a1ng ph\u00e1p ph\u00e2n t\u00edch c\u1ed1t l\u00f5i v\u00e0 \u1ee9ng d\u1ee5ng gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh<\/h3>\n<ul style=\"padding-left: 20px;\">\n<li><strong>C\u00e1c ph\u01b0\u01a1ng ph\u00e1p ch\u00ednh:<\/strong>\n<ol>\n<li><strong>Ph\u01b0\u01a1ng ph\u00e1p \u0111\u1eb7t nh\u00e2n t\u1eed chung:<\/strong> T\u00ecm nh\u00e2n t\u1eed chung l\u00e0 \u01b0\u1edbc chung c\u1ee7a c\u00e1c h\u1ec7 s\u1ed1 v\u00e0 ch\u1ee9a bi\u1ebfn xu\u1ea5t hi\u1ec7n \u1edf m\u1ecdi h\u1ea1ng t\u1eed.<\/li>\n<li><strong>Ph\u01b0\u01a1ng ph\u00e1p d\u00f9ng h\u1eb1ng \u0111\u1eb3ng th\u1ee9c:<\/strong> Bi\u1ec3u di\u1ec5n \u0111a th\u1ee9c v\u1ec1 d\u1ea1ng c\u00e1c h\u1eb1ng \u0111\u1eb3ng th\u1ee9c \u0111\u00e1ng nh\u1edb \u0111\u1ec3 thu g\u1ecdn th\u00e0nh t\u00edch.<\/li>\n<li><strong>Ph\u01b0\u01a1ng ph\u00e1p nh\u00f3m h\u1ea1ng t\u1eed:<\/strong> Nh\u00f3m c\u00e1c h\u1ea1ng t\u1eed th\u00edch h\u1ee3p \u0111\u1ec3 xu\u1ea5t hi\u1ec7n nh\u00e2n t\u1eed chung ho\u1eb7c h\u1eb1ng \u0111\u1eb3ng th\u1ee9c.<\/li>\n<li><strong>Ph\u1ed1i h\u1ee3p nhi\u1ec1u ph\u01b0\u01a1ng ph\u00e1p:<\/strong> V\u1eadn d\u1ee5ng linh ho\u1ea1t c\u00e1c ph\u01b0\u01a1ng ph\u00e1p tr\u00ean theo th\u1ee9 t\u1ef1 \u01b0u ti\u00ean (\u0111\u1eb7t nh\u00e2n t\u1eed chung tr\u01b0\u1edbc, d\u00f9ng h\u1eb1ng \u0111\u1eb3ng th\u1ee9c ho\u1eb7c nh\u00f3m sau).<\/li>\n<\/ol>\n<\/li>\n<li><strong>D\u1ea1ng t\u00ecm x b\u1eb1ng c\u00e1ch \u0111\u01b0a v\u1ec1 t\u00edch b\u1eb1ng 0:<\/strong> Bi\u1ebfn \u0111\u1ed5i ph\u01b0\u01a1ng tr\u00ecnh v\u1ec1 d\u1ea1ng t\u00edch c\u00e1c \u0111a th\u1ee9c b\u1eb1ng 0 (v\u1edbi t\u00ednh ch\u1ea5t n\u1ebfu A \u00b7 B = 0 th\u00ec A = 0 ho\u1eb7c B = 0).<\/li>\n<\/ul>\n<p><!-- H\u1ed8P L\u1ed6I SAI TH\u01af\u1edcNG G\u1eb6P --><\/p>\n<div style=\"background-color: #fff5f5; border-left: 4px solid #e53e3e; padding: 14px 18px; border-radius: 4px; margin: 18px 0;\">\n<p style=\"margin: 0 0 6px 0; font-weight: bold; color: #c53030;\">\u26a0\ufe0f L\u1ed7i sai th\u01b0\u1eddng g\u1eb7p khi ph\u00e2n t\u00edch nh\u00e2n t\u1eed:<\/p>\n<ul style=\"margin: 0; padding-left: 20px; font-size: 15px;\">\n<li>D\u1eebng l\u1ea1i gi\u1eefa ch\u1eebng (ch\u01b0a ph\u00e2n t\u00edch tri\u1ec7t \u0111\u1ec3 \u0111a th\u1ee9c th\u00e0nh nh\u00e2n t\u1eed \u0111\u1ebfn m\u1ee9c t\u1ed1i gi\u1ea3n) ho\u1eb7c nh\u1ea7m d\u1ea5u khi \u0111\u1ed5i d\u1ea5u trong ph\u01b0\u01a1ng ph\u00e1p nh\u00f3m h\u1ea1ng t\u1eed.<\/li>\n<\/ul>\n<\/div>\n<p><!-- V\u00cd D\u1ee4 M\u1eaaU --><\/p>\n<div style=\"background-color: #f7fafc; border-left: 4px solid #0056b3; padding: 16px 20px; border-radius: 4px; margin: 18px 0;\">\n<p style=\"font-weight: bold; color: #0056b3; margin: 0 0 8px 0;\">V\u00ed d\u1ee5 m\u1eabu gi\u1ea3i chi ti\u1ebft: Ph\u00e2n t\u00edch \u0111a th\u1ee9c v\u00e0 t\u00ecm x<\/p>\n<p style=\"margin: 0 0 6px 0;\"><strong>\u0110\u1ec1 b\u00e0i:<\/strong><br \/>\na) Ph\u00e2n t\u00edch \u0111a th\u1ee9c th\u00e0nh nh\u00e2n t\u1eed: <code>P = x<sup>3<\/sup> - 4x<\/code>.<br \/>\nb) T\u00ecm x, bi\u1ebft: <code>x<sup>3<\/sup> - 4x = 0<\/code>.<\/p>\n<p style=\"margin: 0;\"><strong>L\u1eddi gi\u1ea3i chi ti\u1ebft:<\/strong><br \/>\n\u2022 X\u00e9t \u00fd a:<br \/>\n&#8211; \u0110\u1eb7t nh\u00e2n t\u1eed chung x ra ngo\u00e0i: <code>P = x \u00b7 (x<sup>2<\/sup> - 4)<\/code>.<br \/>\n&#8211; \u00c1p d\u1ee5ng h\u1eb1ng \u0111\u1eb3ng th\u1ee9c hi\u1ec7u hai b\u00ecnh ph\u01b0\u01a1ng cho bi\u1ec3u th\u1ee9c trong ngo\u1eb7c: <code>x<sup>2<\/sup> - 4 = (x - 2)(x + 2)<\/code>.<br \/>\n&#8211; K\u1ebft qu\u1ea3 ph\u00e2n t\u00edch: <code>P = x(x - 2)(x + 2)<\/code>.<br \/>\n\u2022 X\u00e9t \u00fd b:<br \/>\n&#8211; T\u1eeb ph\u01b0\u01a1ng tr\u00ecnh <code>x<sup>3<\/sup> - 4x = 0<\/code>, ta \u0111\u01b0a v\u1ec1 d\u1ea1ng t\u00edch v\u1eeba ph\u00e2n t\u00edch:<\/p>\n<p style=\"margin: 0;\"><code>x(x - 2)(x + 2) = 0<\/code>.<br \/>\n&#8211; Suy ra ba tr\u01b0\u1eddng h\u1ee3p:<br \/>\n+ <code>x = 0<\/code><br \/>\n+ <code>x - 2 = 0<\/code> t\u01b0\u01a1ng \u0111\u01b0\u01a1ng <code>x = 2<\/code><br \/>\n+ <code>x + 2 = 0<\/code> t\u01b0\u01a1ng \u0111\u01b0\u01a1ng <code>x = -2<\/code>.<br \/>\n\u2022 <strong>\u0110\u00e1p s\u1ed1:<\/strong> a) \u0110a th\u1ee9c ph\u00e2n t\u00edch th\u00e0nh <code>x(x - 2)(x + 2)<\/code> ; b) x nh\u1eadn c\u00e1c gi\u00e1 tr\u1ecb <code>0, 2, -2<\/code>.<\/p>\n<\/div>\n<p><!-- CH\u1ee6 \u0110\u1ec0 7: CH\u1ee8NG MINH BI\u1ec2U TH\u1ee8C KH\u00d4NG PH\u1ee4 THU\u1ed8C V\u00c0O BI\u1ebeN --><\/p>\n<h2 id=\"muc-9-chung-minh-bieu-thuc-khong-phu-thuoc-vao-bien\" style=\"color: #0056b3; border-bottom: 2px solid #e2e8f0; padding-bottom: 8px; margin-top: 35px; font-size: 20px;\">Ch\u1ee9ng minh bi\u1ec3u th\u1ee9c kh\u00f4ng ph\u1ee5 thu\u1ed9c v\u00e0o bi\u1ebfn<\/h2>\n<h3 style=\"color: #2b6cb0; font-size: 17px; margin-top: 20px;\">Ph\u01b0\u01a1ng ph\u00e1p gi\u1ea3i to\u00e1n v\u00e0 v\u00ed d\u1ee5 minh h\u1ecda<\/h3>\n<ul style=\"padding-left: 20px;\">\n<li><strong>Ph\u01b0\u01a1ng ph\u00e1p gi\u1ea3i:<\/strong>\n<ol>\n<li>Th\u1ef1c hi\u1ec7n c\u00e1c ph\u00e9p t\u00ednh khai tri\u1ec3n h\u1eb1ng \u0111\u1eb3ng th\u1ee9c, nh\u00e2n \u0111a th\u1ee9c, ph\u00e1 ngo\u1eb7c v\u00e0 thu g\u1ecdn bi\u1ec3u th\u1ee9c \u0111\u1ea1i s\u1ed1.<\/li>\n<li>R\u00fat g\u1ecdn c\u00e1c s\u1ed1 h\u1ea1ng ch\u1ee9a bi\u1ebfn (tri\u1ec7t ti\u00eau h\u1ebft c\u00e1c \u1ea9n x, y, &#8230;).<\/li>\n<li>K\u1ebft qu\u1ea3 cu\u1ed1i c\u00f9ng thu \u0111\u01b0\u1ee3c l\u00e0 m\u1ed9t h\u1eb1ng s\u1ed1 (m\u1ed9t s\u1ed1 th\u1ef1c \u0111\u1ed9c l\u1eadp kh\u00f4ng ch\u1ee9a bi\u1ebfn). T\u1eeb \u0111\u00f3 suy ra bi\u1ec3u th\u1ee9c kh\u00f4ng ph\u1ee5 thu\u1ed9c v\u00e0o gi\u00e1 tr\u1ecb c\u1ee7a bi\u1ebfn.<\/li>\n<\/ol>\n<\/li>\n<\/ul>\n<p><!-- H\u1ed8P L\u1ed6I SAI TH\u01af\u1edcNG G\u1eb6P --><\/p>\n<div style=\"background-color: #fff5f5; border-left: 4px solid #e53e3e; padding: 14px 18px; border-radius: 4px; margin: 18px 0;\">\n<p style=\"margin: 0 0 6px 0; font-weight: bold; color: #c53030;\">\u26a0\ufe0f L\u1ed7i sai th\u01b0\u1eddng g\u1eb7p khi ch\u1ee9ng minh bi\u1ec3u th\u1ee9c:<\/p>\n<ul style=\"margin: 0; padding-left: 20px; font-size: 15px;\">\n<li>Nh\u1ea7m d\u1ea5u khi ph\u00e1 ngo\u1eb7c tr\u01b0\u1edbc m\u1ed9t bi\u1ec3u th\u1ee9c c\u00f3 d\u1ea5u tr\u1eeb, d\u1eabn \u0111\u1ebfn vi\u1ec7c c\u00e1c h\u1ea1ng t\u1eed ch\u1ee9a bi\u1ebfn kh\u00f4ng tri\u1ec7t ti\u00eau \u0111\u01b0\u1ee3c h\u1ebft v\u1edbi nhau.<\/li>\n<\/ul>\n<\/div>\n<p><!-- V\u00cd D\u1ee4 M\u1eaaU 1 --><\/p>\n<div style=\"background-color: #f7fafc; border-left: 4px solid #0056b3; padding: 16px 20px; border-radius: 4px; margin: 18px 0;\">\n<p style=\"font-weight: bold; color: #0056b3; margin: 0 0 8px 0;\">V\u00ed d\u1ee5 m\u1eabu 1: Ch\u1ee9ng minh bi\u1ec3u th\u1ee9c kh\u00f4ng ph\u1ee5 thu\u1ed9c v\u00e0o bi\u1ebfn<\/p>\n<p style=\"margin: 0 0 6px 0;\"><strong>\u0110\u1ec1 b\u00e0i:<\/strong> Ch\u1ee9ng minh r\u1eb1ng gi\u00e1 tr\u1ecb c\u1ee7a bi\u1ec3u th\u1ee9c sau kh\u00f4ng ph\u1ee5 thu\u1ed9c v\u00e0o bi\u1ebfn x:<br \/>\n<code>M = (x - 1)<sup>3<\/sup> - (x + 1)<sup>3<\/sup> + 6x<sup>2<\/sup><\/code>.<\/p>\n<p style=\"margin: 0;\"><strong>L\u1eddi gi\u1ea3i chi ti\u1ebft:<\/strong><br \/>\n\u2022 Khai tri\u1ec3n c\u00e1c h\u1eb1ng \u0111\u1eb3ng th\u1ee9c l\u1eadp ph\u01b0\u01a1ng:<br \/>\n&#8211; <code>(x - 1)<sup>3<\/sup> = x<sup>3<\/sup> - 3x<sup>2<\/sup> + 3x - 1<\/code><br \/>\n&#8211; <code>(x + 1)<sup>3<\/sup> = x<sup>3<\/sup> + 3x<sup>2<\/sup> + 3x + 1<\/code><br \/>\n\u2022 Thay v\u00e0o bi\u1ec3u th\u1ee9c M v\u00e0 ch\u00fa \u00fd d\u1ea5u tr\u1eeb tr\u01b0\u1edbc ngo\u1eb7c:<br \/>\n<code>M = (x<sup>3<\/sup> - 3x<sup>2<\/sup> + 3x - 1) - (x<sup>3<\/sup> + 3x<sup>2<\/sup> + 3x + 1) + 6x<sup>2<\/sup><\/code><\/p>\n<p style=\"margin: 0;\"><code>M = x<sup>3<\/sup> - 3x<sup>2<\/sup> + 3x - 1 - x<sup>3<\/sup> - 3x<sup>2<\/sup> - 3x - 1 + 6x<sup>2<\/sup><\/code>.<br \/>\n\u2022 Nh\u00f3m c\u00e1c h\u1ea1ng t\u1eed \u0111\u1ed3ng d\u1ea1ng v\u00e0 thu g\u1ecdn:<br \/>\n<code>M = (x<sup>3<\/sup> - x<sup>3<\/sup>) + (-3x<sup>2<\/sup> - 3x<sup>2<\/sup> + 6x<sup>2<\/sup>) + (3x - 3x) + (-1 - 1) = -2<\/code>.<br \/>\n\u2022 <strong>\u0110\u00e1p s\u1ed1:<\/strong> M = -2, kh\u00f4ng ph\u1ee5 thu\u1ed9c v\u00e0o x.<\/p>\n<\/div>\n<p><!-- V\u00cd D\u1ee4 M\u1eaaU 2 --><\/p>\n<div style=\"background-color: #f7fafc; border-left: 4px solid #0056b3; padding: 16px 20px; border-radius: 4px; margin: 18px 0;\">\n<p style=\"font-weight: bold; color: #0056b3; margin: 0 0 8px 0;\">V\u00ed d\u1ee5 m\u1eabu 2: Ch\u1ee9ng minh bi\u1ec3u th\u1ee9c kh\u00f4ng ph\u1ee5 thu\u1ed9c v\u00e0o bi\u1ebfn<\/p>\n<p style=\"margin: 0 0 6px 0;\"><strong>\u0110\u1ec1 b\u00e0i:<\/strong> Ch\u1ee9ng minh r\u1eb1ng gi\u00e1 tr\u1ecb c\u1ee7a bi\u1ec3u th\u1ee9c sau kh\u00f4ng ph\u1ee5 thu\u1ed9c v\u00e0o bi\u1ebfn x:<br \/>\n<code>N = (x + 2)<sup>2<\/sup> - (x - 2)<sup>2<\/sup> - 8x<\/code>.<\/p>\n<p style=\"margin: 0;\"><strong>L\u1eddi gi\u1ea3i chi ti\u1ebft:<\/strong><br \/>\n\u2022 Khai tri\u1ec3n c\u00e1c h\u1eb1ng \u0111\u1eb3ng th\u1ee9c b\u00ecnh ph\u01b0\u01a1ng ho\u1eb7c d\u00f9ng hi\u1ec7u hai b\u00ecnh ph\u01b0\u01a1ng:<br \/>\n&#8211; <code>(x + 2)<sup>2<\/sup> = x<sup>2<\/sup> + 4x + 4<\/code><br \/>\n&#8211; <code>(x - 2)<sup>2<\/sup> = x<sup>2<\/sup> - 4x + 4<\/code><br \/>\n\u2022 Thay v\u00e0o bi\u1ec3u th\u1ee9c N:<br \/>\n<code>N = (x<sup>2<\/sup> + 4x + 4) - (x<sup>2<\/sup> - 4x + 4) - 8x<\/code><\/p>\n<p style=\"margin: 0;\"><code>N = x<sup>2<\/sup> + 4x + 4 - x<sup>2<\/sup> + 4x - 4 - 8x<\/code>.<br \/>\n\u2022 Nh\u00f3m c\u00e1c h\u1ea1ng t\u1eed \u0111\u1ed3ng d\u1ea1ng v\u00e0 thu g\u1ecdn:<br \/>\n<code>N = (x<sup>2<\/sup> - x<sup>2<\/sup>) + (4x + 4x - 8x) + (4 - 4) = 0<\/code>.<br \/>\n\u2022 <strong>\u0110\u00e1p s\u1ed1:<\/strong> N = 0, kh\u00f4ng ph\u1ee5 thu\u1ed9c v\u00e0o x.<\/p>\n<\/div>\n<\/div>\n<p><!-- K\u1ebeT TH\u00daC: PH\u1ea6N I (TI\u1ebeP THEO) - H\u1eb0NG \u0110\u1eb2NG TH\u1ee8C V\u00c0 PH\u00c2N T\u00cdCH \u0110A TH\u1ee8C TO\u00c1N 8 --><\/p>\n<p><!-- B\u1eaeT \u0110\u1ea6U: PH\u1ea6N II - T\u1ee8 GI\u00c1C TO\u00c1N 8 --><\/p>\n<div class=\"naviedu-content-section\" style=\"font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif; line-height: 1.8; color: #2d3748; font-size: 16px;\">\n<p><!-- BANNER PH\u1ea6N II --><\/p>\n<div style=\"background: linear-gradient(135deg, #0056b3, #0080ff); color: #ffffff; padding: 18px 24px; border-radius: 8px; margin-top: 35px; margin-bottom: 30px;\">\n<h2 id=\"muc-10-phan-ii-tu-giac\" style=\"color: #ffffff; margin: 0; font-size: 22px; text-transform: uppercase; letter-spacing: 0.5px;\">Ph\u1ea7n II: T\u1ee9 Gi\u00e1c<\/h2>\n<\/div>\n<p><!-- CH\u1ee6 \u0110\u1ec0 1: T\u1ee8 GI\u00c1C --><\/p>\n<p style=\"margin: 0 0 16px 0;\">Ph\u1ea7n h\u00ecnh h\u1ecdc trong \u0111\u1ec1 c\u01b0\u01a1ng \u00f4n t\u1eadp gi\u1eefa k\u00ec 1 To\u00e1n 8 xoay quanh c\u00e1c t\u1ee9 gi\u00e1c \u0111\u1eb7c bi\u1ec7t. H\u00e3y h\u1ecdc k\u0129 d\u1ea5u hi\u1ec7u nh\u1eadn bi\u1ebft c\u1ee7a t\u1eebng h\u00ecnh, v\u00ec b\u00e0i ch\u1ee9ng minh t\u1ee9 gi\u00e1c g\u1ea7n nh\u01b0 lu\u00f4n c\u00f3 trong \u0111\u1ec1.<\/p>\n<h2 id=\"muc-11-tu-giac\" style=\"color: #0056b3; border-bottom: 2px solid #e2e8f0; padding-bottom: 8px; margin-top: 35px; font-size: 20px;\">T\u1ee9 gi\u00e1c<\/h2>\n<h3 style=\"color: #2b6cb0; font-size: 17px; margin-top: 20px;\">T\u1ee9 gi\u00e1c l\u1ed3i v\u00e0 \u0111\u1ecbnh l\u00ed t\u1ed5ng s\u1ed1 \u0111o c\u00e1c g\u00f3c<\/h3>\n<ul style=\"padding-left: 20px;\">\n<li><strong>Kh\u00e1i ni\u1ec7m t\u1ee9 gi\u00e1c:<\/strong> T\u1ee9 gi\u00e1c l\u1ed3i l\u00e0 h\u00ecnh \u0111a gi\u00e1c c\u00f3 4 \u0111\u1ec9nh m\u00e0 lu\u00f4n n\u1eb1m v\u1ec1 m\u1ed9t ph\u00eda c\u1ee7a \u0111\u01b0\u1eddng th\u1eb3ng ch\u1ee9a b\u1ea5t k\u1ef3 c\u1ea1nh n\u00e0o c\u1ee7a h\u00ecnh \u0111\u00f3. Trong ch\u01b0\u01a1ng tr\u00ecnh l\u1edbp 8, khi n\u00f3i \u0111\u1ebfn t\u1ee9 gi\u00e1c m\u00e0 kh\u00f4ng ch\u00fa th\u00edch g\u00ec th\u00eam, ta hi\u1ec3u \u0111\u00f3 l\u00e0 t\u1ee9 gi\u00e1c l\u1ed3i.<\/li>\n<li><strong>\u0110\u1ecbnh l\u00ed t\u1ed5ng c\u00e1c g\u00f3c c\u1ee7a m\u1ed9t t\u1ee9 gi\u00e1c:<\/strong> T\u1ed5ng s\u1ed1 \u0111o c\u00e1c g\u00f3c c\u1ee7a m\u1ed9t t\u1ee9 gi\u00e1c lu\u00f4n b\u1eb1ng <code>360\u00b0<\/code> (t\u1ee9c l\u00e0 g\u00f3c A + g\u00f3c B + g\u00f3c C + g\u00f3c D = 360\u00b0).<\/li>\n<\/ul>\n<p><!-- H\u1ed8P L\u1ed6I SAI TH\u01af\u1edcNG G\u1eb6P --><\/p>\n<div style=\"background-color: #fff5f5; border-left: 4px solid #e53e3e; padding: 14px 18px; border-radius: 4px; margin: 18px 0;\">\n<p style=\"margin: 0 0 6px 0; font-weight: bold; color: #c53030;\">\u26a0\ufe0f L\u1ed7i sai th\u01b0\u1eddng g\u1eb7p v\u1ec1 t\u1ed5ng s\u1ed1 \u0111o g\u00f3c:<\/p>\n<ul style=\"margin: 0; padding-left: 20px; font-size: 15px;\">\n<li>Nh\u1ea7m l\u1eabn t\u1ed5ng s\u1ed1 \u0111o c\u00e1c g\u00f3c c\u1ee7a t\u1ee9 gi\u00e1c (360\u00b0) v\u1edbi t\u1ed5ng s\u1ed1 \u0111o c\u00e1c g\u00f3c c\u1ee7a tam gi\u00e1c (180\u00b0), d\u1eabn \u0111\u1ebfn t\u00ednh sai s\u1ed1 \u0111o g\u00f3c c\u00f2n l\u1ea1i.<\/li>\n<\/ul>\n<\/div>\n<p><!-- V\u00cd D\u1ee4 M\u1eaaU --><\/p>\n<div style=\"background-color: #f7fafc; border-left: 4px solid #0056b3; padding: 16px 20px; border-radius: 4px; margin: 18px 0;\">\n<p style=\"font-weight: bold; color: #0056b3; margin: 0 0 8px 0;\">V\u00ed d\u1ee5 m\u1eabu gi\u1ea3i chi ti\u1ebft: T\u00ednh s\u1ed1 \u0111o g\u00f3c c\u00f2n l\u1ea1i c\u1ee7a t\u1ee9 gi\u00e1c<\/p>\n<p style=\"margin: 0 0 6px 0;\"><strong>\u0110\u1ec1 b\u00e0i:<\/strong> Cho t\u1ee9 gi\u00e1c ABCD c\u00f3 s\u1ed1 \u0111o g\u00f3c A = 80\u00b0, g\u00f3c B = 100\u00b0, g\u00f3c C = 120\u00b0. T\u00ednh s\u1ed1 \u0111o c\u1ee7a g\u00f3c D.<\/p>\n<p style=\"margin: 0;\"><strong>L\u1eddi gi\u1ea3i chi ti\u1ebft:<\/strong><br \/>\n\u2022 \u00c1p d\u1ee5ng \u0111\u1ecbnh l\u00ed t\u1ed5ng s\u1ed1 \u0111o c\u00e1c g\u00f3c c\u1ee7a m\u1ed9t t\u1ee9 gi\u00e1c b\u1eb1ng 360\u00b0:<br \/>\n<code>g\u00f3c A + g\u00f3c B + g\u00f3c C + g\u00f3c D = 360\u00b0<\/code>.<br \/>\n\u2022 Thay s\u1ed1 \u0111o c\u00e1c g\u00f3c \u0111\u00e3 bi\u1ebft v\u00e0o bi\u1ec3u th\u1ee9c:<br \/>\n<code>80\u00b0 + 100\u00b0 + 120\u00b0 + g\u00f3c D = 360\u00b0<\/code><br \/>\n<code>300\u00b0 + g\u00f3c D = 360\u00b0<\/code>.<br \/>\n\u2022 Suy ra s\u1ed1 \u0111o g\u00f3c D:<br \/>\n<code>g\u00f3c D = 360\u00b0 - 300\u00b0 = 60\u00b0<\/code>.<br \/>\n\u2022 <strong>\u0110\u00e1p s\u1ed1:<\/strong> <strong>g\u00f3c D = 60\u00b0<\/strong>.<\/p>\n<\/div>\n<p><!-- CH\u1ee6 \u0110\u1ec0 2: H\u00ccNH THANG C\u00c2N --><\/p>\n<h2 id=\"muc-12-hinh-thang-can\" style=\"color: #0056b3; border-bottom: 2px solid #e2e8f0; padding-bottom: 8px; margin-top: 35px; font-size: 20px;\">H\u00ecnh thang c\u00e2n<\/h2>\n<h3 style=\"color: #2b6cb0; font-size: 17px; margin-top: 20px;\">\u0110\u1ecbnh ngh\u0129a, t\u00ednh ch\u1ea5t v\u00e0 d\u1ea5u hi\u1ec7u nh\u1eadn bi\u1ebft<\/h3>\n<ul style=\"padding-left: 20px;\">\n<li><strong>\u0110\u1ecbnh ngh\u0129a:<\/strong> H\u00ecnh thang c\u00e2n l\u00e0 h\u00ecnh thang c\u00f3 hai g\u00f3c k\u1ec1 m\u1ed9t \u0111\u00e1y b\u1eb1ng nhau.<\/li>\n<li><strong>T\u00ednh ch\u1ea5t:<\/strong>\n<ul>\n<li>Trong h\u00ecnh thang c\u00e2n, hai c\u1ea1nh b\u00ean b\u1eb1ng nhau.<\/li>\n<li>Trong h\u00ecnh thang c\u00e2n, hai \u0111\u01b0\u1eddng ch\u00e9o b\u1eb1ng nhau.<\/li>\n<\/ul>\n<\/li>\n<li><strong>D\u1ea5u hi\u1ec7u nh\u1eadn bi\u1ebft:<\/strong>\n<ol>\n<li>H\u00ecnh thang c\u00f3 hai g\u00f3c k\u1ec1 m\u1ed9t \u0111\u00e1y b\u1eb1ng nhau l\u00e0 h\u00ecnh thang c\u00e2n.<\/li>\n<li>H\u00ecnh thang c\u00f3 hai \u0111\u01b0\u1eddng ch\u00e9o b\u1eb1ng nhau l\u00e0 h\u00ecnh thang c\u00e2n.<\/li>\n<\/ol>\n<\/li>\n<\/ul>\n<p><!-- H\u1ed8P L\u1ed6I SAI TH\u01af\u1edcNG G\u1eb6P --><\/p>\n<div style=\"background-color: #fff5f5; border-left: 4px solid #e53e3e; padding: 14px 18px; border-radius: 4px; margin: 18px 0;\">\n<p style=\"margin: 0 0 6px 0; font-weight: bold; color: #c53030;\">\u26a0\ufe0f L\u1ed7i sai th\u01b0\u1eddng g\u1eb7p v\u1ec1 h\u00ecnh thang c\u00e2n:<\/p>\n<ul style=\"margin: 0; padding-left: 20px; font-size: 15px;\">\n<li>Ng\u1ed9 nh\u1eadn r\u1eb1ng b\u1ea5t k\u1ef3 h\u00ecnh thang n\u00e0o c\u00f3 hai c\u1ea1nh b\u00ean b\u1eb1ng nhau c\u0169ng l\u00e0 h\u00ecnh thang c\u00e2n (trong khi th\u1ef1c t\u1ebf h\u00ecnh thang c\u00f3 hai c\u1ea1nh b\u00ean b\u1eb1ng nhau ch\u01b0a ch\u1eafc \u0111\u00e3 l\u00e0 h\u00ecnh thang c\u00e2n, v\u00ed d\u1ee5 h\u00ecnh thang c\u00e2n ph\u1ea3i x\u00e9t hai g\u00f3c k\u1ec1 m\u1ed9t \u0111\u00e1y ho\u1eb7c hai \u0111\u01b0\u1eddng ch\u00e9o b\u1eb1ng nhau).<\/li>\n<\/ul>\n<\/div>\n<p><!-- V\u00cd D\u1ee4 M\u1eaaU --><\/p>\n<div style=\"background-color: #f7fafc; border-left: 4px solid #0056b3; padding: 16px 20px; border-radius: 4px; margin: 18px 0;\">\n<p style=\"font-weight: bold; color: #0056b3; margin: 0 0 8px 0;\">V\u00ed d\u1ee5 m\u1eabu gi\u1ea3i chi ti\u1ebft: T\u00ednh s\u1ed1 \u0111o c\u00e1c g\u00f3c c\u1ee7a h\u00ecnh thang c\u00e2n<\/p>\n<p style=\"margin: 0 0 6px 0;\"><strong>\u0110\u1ec1 b\u00e0i:<\/strong> Cho h\u00ecnh thang c\u00e2n ABCD (v\u1edbi AB song song v\u1edbi CD) c\u00f3 s\u1ed1 \u0111o g\u00f3c A = 70\u00b0. T\u00ednh s\u1ed1 \u0111o c\u00e1c g\u00f3c B, g\u00f3c C v\u00e0 g\u00f3c D c\u1ee7a h\u00ecnh thang c\u00e2n \u0111\u00f3.<\/p>\n<p style=\"margin: 0;\"><strong>L\u1eddi gi\u1ea3i chi ti\u1ebft:<\/strong><br \/>\n\u2022 V\u00ec AB song song v\u1edbi CD n\u00ean h\u00ecnh thang ABCD c\u00f3 c\u00e1c g\u00f3c k\u1ec1 m\u1ed9t c\u1ea1nh b\u00ean b\u00f9 nhau:<br \/>\n&#8211; G\u00f3c A v\u00e0 g\u00f3c D l\u00e0 hai g\u00f3c k\u1ec1 c\u1ea1nh b\u00ean AD, do \u0111\u00f3:<\/p>\n<p style=\"margin: 0;\"><code>g\u00f3c A + g\u00f3c D = 180\u00b0<\/code>.<br \/>\n&#8211; Suy ra <code>g\u00f3c D = 180\u00b0 - 70\u00b0 = 110\u00b0<\/code>.<br \/>\n\u2022 Theo t\u00ednh ch\u1ea5t h\u00ecnh thang c\u00e2n (hai g\u00f3c k\u1ec1 m\u1ed9t \u0111\u00e1y b\u1eb1ng nhau):<br \/>\n&#8211; G\u00f3c k\u1ec1 \u0111\u00e1y l\u1edbn CD l\u00e0 g\u00f3c C b\u1eb1ng v\u1edbi g\u00f3c D, suy ra <code>g\u00f3c C = 110\u00b0<\/code>.<br \/>\n&#8211; G\u00f3c k\u1ec1 \u0111\u00e1y l\u1edbn CD c\u00f2n l\u1ea1i l\u00e0 g\u00f3c B b\u1eb1ng v\u1edbi g\u00f3c A, suy ra <code>g\u00f3c B = 70\u00b0<\/code>.<br \/>\n\u2022 <strong>\u0110\u00e1p s\u1ed1:<\/strong> <strong>g\u00f3c B = 70\u00b0, g\u00f3c C = 110\u00b0, g\u00f3c D = 110\u00b0<\/strong>.<\/p>\n<\/div>\n<p><!-- CH\u1ee6 \u0110\u1ec0 3: H\u00ccNH B\u00ccNH H\u00c0NH --><\/p>\n<h2 id=\"muc-13-hinh-binh-hanh\" style=\"color: #0056b3; border-bottom: 2px solid #e2e8f0; padding-bottom: 8px; margin-top: 35px; font-size: 20px;\">H\u00ecnh b\u00ecnh h\u00e0nh<\/h2>\n<h3 style=\"color: #2b6cb0; font-size: 17px; margin-top: 20px;\">\u0110\u1ecbnh ngh\u0129a, t\u00ednh ch\u1ea5t v\u00e0 5 d\u1ea5u hi\u1ec7u nh\u1eadn bi\u1ebft<\/h3>\n<ul style=\"padding-left: 20px;\">\n<li><strong>\u0110\u1ecbnh ngh\u0129a:<\/strong> H\u00ecnh b\u00ecnh h\u00e0nh l\u00e0 t\u1ee9 gi\u00e1c c\u00f3 c\u00e1c c\u1ea1nh \u0111\u1ed1i song song.<\/li>\n<li><strong>T\u00ednh ch\u1ea5t:<\/strong> Trong h\u00ecnh b\u00ecnh h\u00e0nh:\n<ul>\n<li>C\u00e1c c\u1ea1nh \u0111\u1ed1i b\u1eb1ng nhau.<\/li>\n<li>C\u00e1c g\u00f3c \u0111\u1ed1i b\u1eb1ng nhau.<\/li>\n<li>Hai \u0111\u01b0\u1eddng ch\u00e9o c\u1eaft nhau t\u1ea1i trung \u0111i\u1ec3m c\u1ee7a m\u1ed7i \u0111\u01b0\u1eddng.<\/li>\n<\/ul>\n<\/li>\n<li><strong>N\u0103m d\u1ea5u hi\u1ec7u nh\u1eadn bi\u1ebft h\u00ecnh b\u00ecnh h\u00e0nh:<\/strong>\n<ol>\n<li>T\u1ee9 gi\u00e1c c\u00f3 c\u00e1c c\u1ea1nh \u0111\u1ed1i song song l\u00e0 h\u00ecnh b\u00ecnh h\u00e0nh.<\/li>\n<li>T\u1ee9 gi\u00e1c c\u00f3 c\u00e1c c\u1ea1nh \u0111\u1ed1i b\u1eb1ng nhau l\u00e0 h\u00ecnh b\u00ecnh h\u00e0nh.<\/li>\n<li>T\u1ee9 gi\u00e1c c\u00f3 hai c\u1ea1nh \u0111\u1ed1i song song v\u00e0 b\u1eb1ng nhau l\u00e0 h\u00ecnh b\u00ecnh h\u00e0nh.<\/li>\n<li>T\u1ee9 gi\u00e1c c\u00f3 c\u00e1c g\u00f3c \u0111\u1ed1i b\u1eb1ng nhau l\u00e0 h\u00ecnh b\u00ecnh h\u00e0nh.<\/li>\n<li>T\u1ee9 gi\u00e1c c\u00f3 hai \u0111\u01b0\u1eddng ch\u00e9o c\u1eaft nhau t\u1ea1i trung \u0111i\u1ec3m c\u1ee7a m\u1ed7i \u0111\u01b0\u1eddng l\u00e0 h\u00ecnh b\u00ecnh h\u00e0nh.<\/li>\n<\/ol>\n<\/li>\n<\/ul>\n<p><!-- H\u1ed8P L\u1ed6I SAI TH\u01af\u1edcNG G\u1eb6P --><\/p>\n<div style=\"background-color: #fff5f5; border-left: 4px solid #e53e3e; padding: 14px 18px; border-radius: 4px; margin: 18px 0;\">\n<p style=\"margin: 0 0 6px 0; font-weight: bold; color: #c53030;\">\u26a0\ufe0f L\u1ed7i sai th\u01b0\u1eddng g\u1eb7p khi ch\u1ee9ng minh h\u00ecnh b\u00ecnh h\u00e0nh:<\/p>\n<ul style=\"margin: 0; padding-left: 20px; font-size: 15px;\">\n<li>Nh\u1ea7m l\u1eabn gi\u1eefa d\u1ea5u hi\u1ec7u &#8220;hai c\u1ea1nh \u0111\u1ed1i song song v\u00e0 b\u1eb1ng nhau&#8221; (\u0111\u00fang l\u00e0 h\u00ecnh b\u00ecnh h\u00e0nh) v\u1edbi &#8220;hai c\u1ea1nh \u0111\u1ed1i b\u1ea5t k\u00ec b\u1eb1ng nhau v\u00e0 hai c\u1ea1nh kia song song&#8221; (ch\u01b0a \u0111\u1ee7 \u0111i\u1ec1u ki\u1ec7n k\u1ebft lu\u1eadn).<\/li>\n<\/ul>\n<\/div>\n<p><!-- V\u00cd D\u1ee4 M\u1eaaU --><\/p>\n<div style=\"background-color: #f7fafc; border-left: 4px solid #0056b3; padding: 16px 20px; border-radius: 4px; margin: 18px 0;\">\n<p style=\"font-weight: bold; color: #0056b3; margin: 0 0 8px 0;\">V\u00ed d\u1ee5 m\u1eabu gi\u1ea3i chi ti\u1ebft: Ch\u1ee9ng minh t\u1ee9 gi\u00e1c l\u00e0 h\u00ecnh b\u00ecnh h\u00e0nh<\/p>\n<p style=\"margin: 0 0 6px 0;\"><strong>\u0110\u1ec1 b\u00e0i:<\/strong> Cho t\u1ee9 gi\u00e1c ABCD c\u00f3 M v\u00e0 N l\u1ea7n l\u01b0\u1ee3t l\u00e0 trung \u0111i\u1ec3m c\u1ee7a hai \u0111\u01b0\u1eddng ch\u00e9o AC v\u00e0 BD. G\u1ecdi O l\u00e0 giao \u0111i\u1ec3m c\u1ee7a hai \u0111o\u1ea1n th\u1eb3ng n\u1ed1i c\u00e1c trung \u0111i\u1ec3m. Ch\u1ee9ng minh r\u1eb1ng t\u1ee9 gi\u00e1c c\u00f3 c\u00e1c c\u1ea1nh \u0111\u1ed1i th\u1ecfa m\u00e3n \u0111i\u1ec1u ki\u1ec7n l\u00e0 h\u00ecnh b\u00ecnh h\u00e0nh b\u1eb1ng c\u00e1ch vi\u1ebft gi\u1ea3 thi\u1ebft &#8211; k\u1ebft lu\u1eadn v\u00e0 l\u1eadp lu\u1eadn.<\/p>\n<p style=\"margin: 0;\"><strong>L\u1eddi gi\u1ea3i chi ti\u1ebft:<\/strong><br \/>\n\u2022 T\u00f3m t\u1eaft Gi\u1ea3 thi\u1ebft &#8211; K\u1ebft lu\u1eadn (GT &#8211; KL):<br \/>\n&#8211; GT: T\u1ee9 gi\u00e1c ABCD, AB song song v\u1edbi CD v\u00e0 AB = CD.<br \/>\n&#8211; KL: <code>T\u1ee9 gi\u00e1c ABCD l\u00e0 h\u00ecnh b\u00ecnh h\u00e0nh<\/code>.<br \/>\n\u2022 Tr\u00ecnh b\u00e0y ch\u1ee9ng minh:<br \/>\n&#8211; X\u00e9t t\u1ee9 gi\u00e1c ABCD c\u00f3 c\u1ea1nh AB song song v\u1edbi CD (theo gi\u1ea3 thi\u1ebft).<br \/>\n&#8211; L\u1ea1i c\u00f3 c\u1ea1nh AB = CD (theo gi\u1ea3 thi\u1ebft).<br \/>\n&#8211; \u00c1p d\u1ee5ng d\u1ea5u hi\u1ec7u nh\u1eadn bi\u1ebft s\u1ed1 3:<\/p>\n<p style=\"margin: 0;\">T\u1ee9 gi\u00e1c c\u00f3 hai c\u1ea1nh \u0111\u1ed1i v\u1eeba song song v\u1eeba b\u1eb1ng nhau l\u00e0 h\u00ecnh b\u00ecnh h\u00e0nh.<br \/>\n&#8211; Do \u0111\u00f3, t\u1ee9 gi\u00e1c ABCD l\u00e0 h\u00ecnh b\u00ecnh h\u00e0nh.<br \/>\n\u2022 <strong>K\u1ebft lu\u1eadn:<\/strong> <strong>\u0110\u00e3 ch\u1ee9ng minh t\u1ee9 gi\u00e1c ABCD l\u00e0 h\u00ecnh b\u00ecnh h\u00e0nh<\/strong>.<\/p>\n<\/div>\n<\/div>\n<p><!-- K\u1ebeT TH\u00daC: PH\u1ea6N II - T\u1ee8 GI\u00c1C TO\u00c1N 8 --><\/p>\n<p><!-- B\u1eaeT \u0110\u1ea6U: PH\u1ea6N II (TI\u1ebeP THEO) - H\u00ccNH CH\u1eee NH\u1eacT, H\u00ccNH THOI V\u00c0 H\u00ccNH VU\u00d4NG TO\u00c1N 8 --><\/p>\n<div class=\"naviedu-content-section\" style=\"font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif; line-height: 1.8; color: #2d3748; font-size: 16px;\">\n<p><!-- CH\u1ee6 \u0110\u1ec0 4: H\u00ccNH CH\u1eee NH\u1eacT --><\/p>\n<h2 id=\"muc-14-hinh-chu-nhat\" style=\"color: #0056b3; border-bottom: 2px solid #e2e8f0; padding-bottom: 8px; margin-top: 35px; font-size: 20px;\">H\u00ecnh ch\u1eef nh\u1eadt<\/h2>\n<h3 style=\"color: #2b6cb0; font-size: 17px; margin-top: 20px;\">\u0110\u1ecbnh ngh\u0129a, t\u00ednh ch\u1ea5t, d\u1ea5u hi\u1ec7u nh\u1eadn bi\u1ebft v\u00e0 \u1ee9ng d\u1ee5ng tam gi\u00e1c vu\u00f4ng<\/h3>\n<ul style=\"padding-left: 20px;\">\n<li><strong>\u0110\u1ecbnh ngh\u0129a:<\/strong> H\u00ecnh ch\u1eef nh\u1eadt l\u00e0 t\u1ee9 gi\u00e1c c\u00f3 b\u1ed1n g\u00f3c vu\u00f4ng.<\/li>\n<li><strong>T\u00ednh ch\u1ea5t:<\/strong> Trong h\u00ecnh ch\u1eef nh\u1eadt, c\u00e1c c\u1ea1nh \u0111\u1ed1i b\u1eb1ng nhau, hai \u0111\u01b0\u1eddng ch\u00e9o b\u1eb1ng nhau v\u00e0 c\u1eaft nhau t\u1ea1i trung \u0111i\u1ec3m c\u1ee7a m\u1ed7i \u0111\u01b0\u1eddng.<\/li>\n<li><strong>D\u1ea5u hi\u1ec7u nh\u1eadn bi\u1ebft:<\/strong>\n<ol>\n<li>T\u1ee9 gi\u00e1c c\u00f3 ba g\u00f3c vu\u00f4ng l\u00e0 h\u00ecnh ch\u1eef nh\u1eadt.<\/li>\n<li>H\u00ecnh thang c\u00e2n c\u00f3 m\u1ed9t g\u00f3c vu\u00f4ng l\u00e0 h\u00ecnh ch\u1eef nh\u1eadt.<\/li>\n<li>H\u00ecnh b\u00ecnh h\u00e0nh c\u00f3 m\u1ed9t g\u00f3c vu\u00f4ng l\u00e0 h\u00ecnh ch\u1eef nh\u1eadt.<\/li>\n<li>H\u00ecnh b\u00ecnh h\u00e0nh c\u00f3 hai \u0111\u01b0\u1eddng ch\u00e9o b\u1eb1ng nhau l\u00e0 h\u00ecnh ch\u1eef nh\u1eadt.<\/li>\n<\/ol>\n<\/li>\n<li><strong>\u00c1p d\u1ee5ng v\u00e0o tam gi\u00e1c vu\u00f4ng:<\/strong> Trong m\u1ed9t tam gi\u00e1c vu\u00f4ng, \u0111\u01b0\u1eddng trung tuy\u1ebfn \u1ee9ng v\u1edbi c\u1ea1nh huy\u1ec1n b\u1eb1ng m\u1ed9t n\u1eeda c\u1ea1nh huy\u1ec1n. Ng\u01b0\u1ee3c l\u1ea1i, n\u1ebfu m\u1ed9t tam gi\u00e1c c\u00f3 \u0111\u01b0\u1eddng trung tuy\u1ebfn \u1ee9ng v\u1edbi m\u1ed9t c\u1ea1nh b\u1eb1ng n\u1eeda c\u1ea1nh \u1ea5y th\u00ec tam gi\u00e1c \u0111\u00f3 l\u00e0 tam gi\u00e1c vu\u00f4ng.<\/li>\n<\/ul>\n<p><!-- H\u1ed8P L\u1ed6I SAI TH\u01af\u1edcNG G\u1eb6P --><\/p>\n<div style=\"background-color: #fff5f5; border-left: 4px solid #e53e3e; padding: 14px 18px; border-radius: 4px; margin: 18px 0;\">\n<p style=\"margin: 0 0 6px 0; font-weight: bold; color: #c53030;\">\u26a0\ufe0f L\u1ed7i sai th\u01b0\u1eddng g\u1eb7p v\u1ec1 h\u00ecnh ch\u1eef nh\u1eadt:<\/p>\n<ul style=\"margin: 0; padding-left: 20px; font-size: 15px;\">\n<li>Qu\u00ean t\u00ednh ch\u1ea5t hai \u0111\u01b0\u1eddng ch\u00e9o b\u1eb1ng nhau c\u1ee7a h\u00ecnh ch\u1eef nh\u1eadt khi gi\u1ea3i c\u00e1c b\u00e0i to\u00e1n li\u00ean quan \u0111\u1ebfn \u0111\u1ed9 d\u00e0i \u0111o\u1ea1n th\u1eb3ng, ho\u1eb7c nh\u1ea7m l\u1eabn t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng trung tuy\u1ebfn trong tam gi\u00e1c vu\u00f4ng.<\/li>\n<\/ul>\n<\/div>\n<p><!-- V\u00cd D\u1ee4 M\u1eaaU --><\/p>\n<div style=\"background-color: #f7fafc; border-left: 4px solid #0056b3; padding: 16px 20px; border-radius: 4px; margin: 18px 0;\">\n<p style=\"font-weight: bold; color: #0056b3; margin: 0 0 8px 0;\">V\u00ed d\u1ee5 m\u1eabu gi\u1ea3i chi ti\u1ebft: \u00c1p d\u1ee5ng t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng trung tuy\u1ebfn trong tam gi\u00e1c vu\u00f4ng<\/p>\n<p style=\"margin: 0 0 6px 0;\"><strong>\u0110\u1ec1 b\u00e0i:<\/strong> Cho tam gi\u00e1c ABC vu\u00f4ng t\u1ea1i A c\u00f3 c\u1ea1nh huy\u1ec1n BC = 10 cm. G\u1ecdi M l\u00e0 trung \u0111i\u1ec3m c\u1ee7a c\u1ea1nh BC. T\u00ednh \u0111\u1ed9 d\u00e0i \u0111o\u1ea1n th\u1eb3ng AM.<\/p>\n<p style=\"margin: 0;\"><strong>L\u1eddi gi\u1ea3i chi ti\u1ebft:<\/strong><br \/>\n\u2022 X\u00e9t tam gi\u00e1c ABC vu\u00f4ng t\u1ea1i A c\u00f3 AM l\u00e0 \u0111\u01b0\u1eddng trung tuy\u1ebfn \u1ee9ng v\u1edbi c\u1ea1nh huy\u1ec1n BC.<br \/>\n\u2022 \u00c1p d\u1ee5ng t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng trung tuy\u1ebfn \u1ee9ng v\u1edbi c\u1ea1nh huy\u1ec1n trong tam gi\u00e1c vu\u00f4ng:<br \/>\n&#8211; \u0110\u1ed9 d\u00e0i \u0111o\u1ea1n th\u1eb3ng trung tuy\u1ebfn \u1ee9ng v\u1edbi c\u1ea1nh huy\u1ec1n b\u1eb1ng m\u1ed9t n\u1eeda c\u1ea1nh huy\u1ec1n: <code>AM = 1\/2 \u00b7 BC<\/code>.<br \/>\n\u2022 Thay s\u1ed1 \u0111o BC = 10 cm v\u00e0o c\u00f4ng th\u1ee9c:<br \/>\n<code>AM = 1\/2 \u00b7 10 = 5 (cm)<\/code>.<br \/>\n\u2022 <strong>K\u1ebft lu\u1eadn:<\/strong> <strong>\u0110\u1ed9 d\u00e0i \u0111o\u1ea1n th\u1eb3ng AM b\u1eb1ng 5 cm<\/strong>.<\/p>\n<\/div>\n<p><!-- CH\u1ee6 \u0110\u1ec0 5: H\u00ccNH THOI V\u00c0 H\u00ccNH VU\u00d4NG --><\/p>\n<h2 id=\"muc-15-hinh-thoi-hinh-vuong\" style=\"color: #0056b3; border-bottom: 2px solid #e2e8f0; padding-bottom: 8px; margin-top: 35px; font-size: 20px;\">H\u00ecnh thoi, h\u00ecnh vu\u00f4ng<\/h2>\n<h3 style=\"color: #2b6cb0; font-size: 17px; margin-top: 20px;\">\u0110\u1ecbnh ngh\u0129a, t\u00ednh ch\u1ea5t, d\u1ea5u hi\u1ec7u v\u00e0 b\u1ea3ng so s\u00e1nh \u0111\u01b0\u1eddng ch\u00e9o<\/h3>\n<ul style=\"padding-left: 20px;\">\n<li><strong>H\u00ecnh thoi:<\/strong> L\u00e0 t\u1ee9 gi\u00e1c c\u00f3 b\u1ed1n c\u1ea1nh b\u1eb1ng nhau.\n<ul>\n<li><em>T\u00ednh ch\u1ea5t:<\/em> Hai \u0111\u01b0\u1eddng ch\u00e9o vu\u00f4ng g\u00f3c v\u1edbi nhau v\u00e0 l\u00e0 c\u00e1c tia ph\u00e2n gi\u00e1c c\u1ee7a c\u00e1c g\u00f3c c\u1ee7a h\u00ecnh thoi.<\/li>\n<li><em>D\u1ea5u hi\u1ec7u nh\u1eadn bi\u1ebft:<\/em> H\u00ecnh b\u00ecnh h\u00e0nh c\u00f3 hai c\u1ea1nh k\u1ec1 b\u1eb1ng nhau (ho\u1eb7c c\u00f3 hai \u0111\u01b0\u1eddng ch\u00e9o vu\u00f4ng g\u00f3c, ho\u1eb7c c\u00f3 m\u1ed9t \u0111\u01b0\u1eddng ch\u00e9o l\u00e0 tia ph\u00e2n gi\u00e1c c\u1ee7a m\u1ed9t g\u00f3c) l\u00e0 h\u00ecnh thoi.<\/li>\n<\/ul>\n<\/li>\n<li><strong>H\u00ecnh vu\u00f4ng:<\/strong> L\u00e0 t\u1ee9 gi\u00e1c c\u00f3 b\u1ed1n g\u00f3c vu\u00f4ng v\u00e0 b\u1ed1n c\u1ea1nh b\u1eb1ng nhau (v\u1eeba l\u00e0 h\u00ecnh ch\u1eef nh\u1eadt v\u1eeba l\u00e0 h\u00ecnh thoi). Do \u0111\u00f3, h\u00ecnh vu\u00f4ng s\u1edf h\u1eefu to\u00e0n b\u1ed9 t\u00ednh ch\u1ea5t c\u1ee7a c\u1ea3 h\u00ecnh ch\u1eef nh\u1eadt v\u00e0 h\u00ecnh thoi.<\/li>\n<\/ul>\n<p><!-- B\u1ea2NG SO S\u00c1NH T\u00cdNH CH\u1ea4T \u0110\u01af\u1edcNG CH\u00c9O --><\/p>\n<h3 style=\"color: #2b6cb0; font-size: 18px; margin-top: 22px;\">B\u1ea3ng so s\u00e1nh t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng ch\u00e9o c\u1ee7a c\u00e1c h\u00ecnh \u0111\u1eb7c bi\u1ec7t<\/h3>\n<div style=\"overflow-x: auto; margin: 15px 0;\">\n<table style=\"table-layout: auto; font-size: 14px; width: 100%; border-collapse: collapse; border: 1px solid #cbd5e0; text-align: left;\">\n<thead style=\"background-color: #edf2f7;\">\n<tr>\n<th style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; color: #0056b3; width: 25%;\">H\u00ecnh \u0111\u1eb7c bi\u1ec7t<\/th>\n<th style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; color: #0056b3; width: 25%;\">C\u1eaft nhau t\u1ea1i trung \u0111i\u1ec3m m\u1ed7i \u0111\u01b0\u1eddng<\/th>\n<th style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; color: #0056b3; width: 25%;\">Hai \u0111\u01b0\u1eddng ch\u00e9o b\u1eb1ng nhau<\/th>\n<th style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; color: #0056b3; width: 25%;\">Hai \u0111\u01b0\u1eddng ch\u00e9o vu\u00f4ng g\u00f3c<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; font-weight: bold;\">H\u00ecnh b\u00ecnh h\u00e0nh<\/td>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; color: #2b6cb0; text-align: center;\">C\u00f3<\/td>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; color: #c53030; text-align: center;\">Kh\u00f4ng<\/td>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; color: #c53030; text-align: center;\">Kh\u00f4ng<\/td>\n<\/tr>\n<tr>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; font-weight: bold;\">H\u00ecnh ch\u1eef nh\u1eadt<\/td>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; color: #2b6cb0; text-align: center;\">C\u00f3<\/td>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; color: #2b6cb0; text-align: center;\">C\u00f3<\/td>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; color: #c53030; text-align: center;\">Kh\u00f4ng<\/td>\n<\/tr>\n<tr>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; font-weight: bold;\">H\u00ecnh thoi<\/td>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; color: #2b6cb0; text-align: center;\">C\u00f3<\/td>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; color: #c53030; text-align: center;\">Kh\u00f4ng<\/td>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; color: #2b6cb0; text-align: center;\">C\u00f3<\/td>\n<\/tr>\n<tr>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; font-weight: bold;\">H\u00ecnh vu\u00f4ng<\/td>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; color: #2b6cb0; text-align: center;\">C\u00f3<\/td>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; color: #2b6cb0; text-align: center;\">C\u00f3<\/td>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; color: #2b6cb0; text-align: center;\">C\u00f3<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p><!-- H\u1ed8P L\u1ed6I SAI TH\u01af\u1edcNG G\u1eb6P --><\/p>\n<div style=\"background-color: #fff5f5; border-left: 4px solid #e53e3e; padding: 14px 18px; border-radius: 4px; margin: 18px 0;\">\n<p style=\"margin: 0 0 6px 0; font-weight: bold; color: #c53030;\">\u26a0\ufe0f L\u1ed7i sai th\u01b0\u1eddng g\u1eb7p v\u1ec1 h\u00ecnh thoi v\u00e0 h\u00ecnh ch\u1eef nh\u1eadt:<\/p>\n<ul style=\"margin: 0; padding-left: 20px; font-size: 15px;\">\n<li>Nh\u1ea7m l\u1eabn t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng ch\u00e9o c\u1ee7a h\u00ecnh thoi (vu\u00f4ng g\u00f3c nh\u01b0ng kh\u00f4ng b\u1eb1ng nhau) v\u1edbi h\u00ecnh ch\u1eef nh\u1eadt (b\u1eb1ng nhau nh\u01b0ng kh\u00f4ng vu\u00f4ng g\u00f3c), trong khi h\u00ecnh vu\u00f4ng h\u1ed9i t\u1ee5 c\u1ea3 hai t\u00ednh ch\u1ea5t n\u00e0y.<\/li>\n<\/ul>\n<\/div>\n<p><!-- V\u00cd D\u1ee4 M\u1eaaU --><\/p>\n<div style=\"background-color: #f7fafc; border-left: 4px solid #0056b3; padding: 16px 20px; border-radius: 4px; margin: 18px 0;\">\n<p style=\"font-weight: bold; color: #0056b3; margin: 0 0 8px 0;\">V\u00ed d\u1ee5 m\u1eabu gi\u1ea3i chi ti\u1ebft: Ch\u1ee9ng minh h\u00ecnh thoi v\u00e0 t\u00ednh \u0111\u1ed9 d\u00e0i<\/p>\n<p style=\"margin: 0 0 6px 0;\"><strong>\u0110\u1ec1 b\u00e0i:<\/strong> Cho h\u00ecnh thoi ABCD c\u00f3 hai \u0111\u01b0\u1eddng ch\u00e9o AC = 6 cm v\u00e0 BD = 8 cm. T\u00ednh \u0111\u1ed9 d\u00e0i c\u1ea1nh c\u1ee7a h\u00ecnh thoi ABCD.<\/p>\n<p style=\"margin: 0;\"><strong>L\u1eddi gi\u1ea3i chi ti\u1ebft:<\/strong><br \/>\n\u2022 G\u1ecdi O l\u00e0 giao \u0111i\u1ec3m c\u1ee7a hai \u0111\u01b0\u1eddng ch\u00e9o AC v\u00e0 BD.<br \/>\n\u2022 V\u00ec ABCD l\u00e0 h\u00ecnh thoi n\u00ean hai \u0111\u01b0\u1eddng ch\u00e9o AC v\u00e0 BD vu\u00f4ng g\u00f3c v\u1edbi nhau t\u1ea1i trung \u0111i\u1ec3m c\u1ee7a m\u1ed7i \u0111\u01b0\u1eddng:<br \/>\n&#8211; \u0110\u1ed9 d\u00e0i \u0111o\u1ea1n OA = AC : 2 = 6 : 2 = 3 (cm).<br \/>\n&#8211; \u0110\u1ed9 d\u00e0i \u0111o\u1ea1n OB = BD : 2 = 8 : 2 = 4 (cm).<br \/>\n\u2022 Tam gi\u00e1c AOB vu\u00f4ng t\u1ea1i O (do AC vu\u00f4ng g\u00f3c v\u1edbi BD).<\/p>\n<p style=\"margin: 0;\">\u00c1p d\u1ee5ng \u0111\u1ecbnh l\u00ed Pythagore trong tam gi\u00e1c vu\u00f4ng AOB:<br \/>\n<code>AB<sup>2<\/sup> = OA<sup>2<\/sup> + OB<sup>2<\/sup> = 3<sup>2<\/sup> + 4<sup>2<\/sup> = 9 + 16 = 25<\/code>.<br \/>\n\u2022 Suy ra \u0111\u1ed9 d\u00e0i c\u1ea1nh h\u00ecnh thoi: <code>AB = c\u0103n b\u1eadc hai c\u1ee7a 25 = 5 (cm)<\/code>.<br \/>\n\u2022 <strong>\u0110\u00e1p s\u1ed1:<\/strong> <strong>\u0110\u1ed9 d\u00e0i c\u1ea1nh c\u1ee7a h\u00ecnh thoi b\u1eb1ng 5 cm<\/strong>.<\/p>\n<\/div>\n<p><!-- L\u01afU \u00dd \/ INTERNAL LINK BOX --><\/p>\n<div style=\"background-color: #edf2f7; border-left: 4px solid #0056b3; padding: 14px 18px; border-radius: 4px; margin-top: 25px;\">\n<p style=\"margin: 0; font-size: 15px; color: #2d3748;\"><strong>\ud83d\udca1 L\u1eddi khuy\u00ean t\u1eeb chuy\u00ean gia NaviEdu:<\/strong> H\u00ecnh h\u1ecdc l\u1edbp 8 l\u00e0 n\u1ec1n t\u1ea3ng t\u01b0 duy ch\u1ee9ng minh s\u1eafc b\u00e9n quy\u1ebft \u0111\u1ecbnh \u0111i\u1ec3m s\u1ed1 m\u00f4n To\u00e1n trong c\u00e1c k\u1ef3 thi l\u1edbn. N\u1ebfu con \u0111ang g\u1eb7p kh\u00f3 kh\u0103n trong vi\u1ec7c nh\u1edb d\u1ea5u hi\u1ec7u nh\u1eadn bi\u1ebft hay tr\u00ecnh b\u00e0y b\u00e0i to\u00e1n h\u00ecnh h\u1ecdc, ba m\u1eb9 h\u00e3y tham kh\u1ea3o ngay l\u1ed9 tr\u00ecnh <a style=\"color: #0056b3; font-weight: bold; text-decoration: underline;\" href=\"https:\/\/navi.edu.vn\/mat-goc-toan\/lop-8\">l\u1ea5y l\u1ea1i g\u1ed1c To\u00e1n 8<\/a> t\u1ea1i NaviEdu \u0111\u1ec3 h\u1ed7 tr\u1ee3 con t\u1ef1 tin b\u1ee9t ph\u00e1 \u0111i\u1ec3m s\u1ed1!<\/p>\n<\/div>\n<\/div>\n<p><!-- K\u1ebeT TH\u00daC: PH\u1ea6N II (TI\u1ebeP THEO) - H\u00ccNH CH\u1eee NH\u1eacT, H\u00ccNH THOI V\u00c0 H\u00ccNH VU\u00d4NG TO\u00c1N 8 --><\/p>\n<p><!-- B\u1eaeT \u0110\u1ea6U PH\u1ea6N III: L\u1ecaCH \u00d4N T\u1eacP 7 NG\u00c0Y & \u0110\u1ec0 THI M\u1eaaU TO\u00c1N 8 --><\/p>\n<div class=\"naviedu-content-section\" style=\"font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif; line-height: 1.8; color: #2d3748; font-size: 16px;\">\n<p><!-- BANNER PH\u1ea6N III --><\/p>\n<div style=\"background: linear-gradient(135deg, #0056b3, #0080ff); color: #ffffff; padding: 18px 24px; border-radius: 8px; margin-top: 35px; margin-bottom: 30px;\">\n<h2 id=\"muc-16-phan-iii-lich-on-tap-7-ngay-de-thi-mau\" style=\"color: #ffffff; margin: 0; font-size: 22px; text-transform: uppercase; letter-spacing: 0.5px;\">Ph\u1ea7n III: L\u1ecbch \u00d4n T\u1eadp 7 Ng\u00e0y &amp; \u0110\u1ec1 Thi M\u1eabu<\/h2>\n<\/div>\n<p><!-- CH\u1ee6 \u0110\u1ec0 1: L\u1ecaCH \u00d4N T\u1eacP 7 NG\u00c0Y --><\/p>\n<p style=\"margin: 0 0 16px 0;\">Khi \u0111\u00e3 \u0111i h\u1ebft c\u00e1c ch\u1ee7 \u0111\u1ec1 trong \u0111\u1ec1 c\u01b0\u01a1ng \u00f4n t\u1eadp gi\u1eefa k\u00ec 1 To\u00e1n 8, ba m\u1eb9 c\u00f3 th\u1ec3 d\u00f9ng l\u1ecbch 7 ng\u00e0y d\u01b0\u1edbi \u0111\u00e2y \u0111\u1ec3 c\u00f9ng con h\u1ec7 th\u1ed1ng l\u1ea1i ki\u1ebfn th\u1ee9c v\u00e0 luy\u1ec7n \u0111\u1ec1 tr\u01b0\u1edbc ng\u00e0y thi.<\/p>\n<h2 id=\"muc-17-lich-on-tap-giua-ki-1-toan-8-trong-7-ngay-giup-con-tu-tin-da\" style=\"color: #0056b3; border-bottom: 2px solid #e2e8f0; padding-bottom: 8px; margin-top: 35px; font-size: 20px;\">L\u1ecbch \u00f4n t\u1eadp gi\u1eefa k\u00ec 1 To\u00e1n 8 trong 7 ng\u00e0y gi\u00fap con t\u1ef1 tin \u0111\u1ea1t \u0111i\u1ec3m cao<\/h2>\n<p>\u0110\u1ec3 gi\u00fap h\u1ecdc sinh THCS \u00f4n luy\u1ec7n hi\u1ec7u qu\u1ea3, n\u1eafm v\u1eefng to\u00e0n b\u1ed9 ki\u1ebfn th\u1ee9c tr\u1ecdng t\u00e2m v\u00e0 l\u00e0m quen v\u1edbi \u00e1p l\u1ef1c ph\u00f2ng thi, \u0111\u1ed9i ng\u0169 chuy\u00ean m\u00f4n t\u1ea1i NaviEdu x\u00e2y d\u1ef1ng th\u1eddi gian bi\u1ec3u \u00f4n t\u1eadp n\u01b0\u1edbc r\u00fat trong 7 ng\u00e0y (m\u1ed7i ng\u00e0y t\u1eeb 45 \u2013 60 ph\u00fat):<\/p>\n<div style=\"overflow-x: auto; margin: 20px 0;\">\n<table style=\"min-width: 640px; table-layout: fixed; font-size: 15px; width: 100%; border-collapse: collapse; border: 1px solid #cbd5e0; text-align: left;\">\n<colgroup>\n<col style=\"width: 16%;\" \/>\n<col style=\"width: 48%;\" \/>\n<col style=\"width: 36%;\" \/><\/colgroup>\n<thead style=\"background-color: #edf2f7;\">\n<tr>\n<th style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 12px 14px; border: 1px solid #cbd5e0; color: #0056b3; width: 18%;\">Th\u1eddi gian<\/th>\n<th style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 12px 14px; border: 1px solid #cbd5e0; color: #0056b3; width: 47%;\">N\u1ed9i dung \u00f4n<\/th>\n<th style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 12px 14px; border: 1px solid #cbd5e0; color: #0056b3; width: 35%;\">M\u1ee5c ti\u00eau (45\u201360 ph\u00fat\/ng\u00e0y)<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 12px 14px; border: 1px solid #cbd5e0; font-weight: bold;\">Ng\u00e0y 1<\/td>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 12px 14px; border: 1px solid #cbd5e0;\">\u0110\u01a1n th\u1ee9c, \u0111a th\u1ee9c nhi\u1ec1u bi\u1ebfn.<\/td>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 12px 14px; border: 1px solid #cbd5e0;\">Th\u00e0nh th\u1ea1o c\u00e1ch thu g\u1ecdn \u0111\u01a1n th\u1ee9c, \u0111a th\u1ee9c, t\u00ecm h\u1ec7 s\u1ed1, ph\u1ea7n bi\u1ebfn v\u00e0 t\u00ednh gi\u00e1 tr\u1ecb bi\u1ec3u th\u1ee9c.<\/td>\n<\/tr>\n<tr>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 12px 14px; border: 1px solid #cbd5e0; font-weight: bold;\">Ng\u00e0y 2<\/td>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 12px 14px; border: 1px solid #cbd5e0;\">C\u1ed9ng, tr\u1eeb, nh\u00e2n, chia \u0111a th\u1ee9c.<\/td>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 12px 14px; border: 1px solid #cbd5e0;\">N\u1eafm ch\u1eafc quy t\u1eafc th\u1ef1c hi\u1ec7n c\u00e1c ph\u00e9p t\u00ednh \u0111\u1ea1i s\u1ed1 v\u00e0 chia \u0111a th\u1ee9c cho \u0111\u01a1n th\u1ee9c ch\u00ednh x\u00e1c.<\/td>\n<\/tr>\n<tr>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 12px 14px; border: 1px solid #cbd5e0; font-weight: bold;\">Ng\u00e0y 3<\/td>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 12px 14px; border: 1px solid #cbd5e0;\">7 h\u1eb1ng \u0111\u1eb3ng th\u1ee9c \u0111\u00e1ng nh\u1edb, t\u00ednh nhanh.<\/td>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 12px 14px; border: 1px solid #cbd5e0;\">Thu\u1ed9c l\u00f2ng v\u00e0 v\u1eadn d\u1ee5ng linh ho\u1ea1t 7 h\u1eb1ng \u0111\u1eb3ng th\u1ee9c v\u00e0o b\u00e0i to\u00e1n khai tri\u1ec3n v\u00e0 t\u00ednh nhanh gi\u00e1 tr\u1ecb.<\/td>\n<\/tr>\n<tr>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 12px 14px; border: 1px solid #cbd5e0; font-weight: bold;\">Ng\u00e0y 4<\/td>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 12px 14px; border: 1px solid #cbd5e0;\">Ph\u00e2n t\u00edch \u0111a th\u1ee9c th\u00e0nh nh\u00e2n t\u1eed, t\u00ecm x, ch\u1ee9ng minh bi\u1ec3u th\u1ee9c kh\u00f4ng ph\u1ee5 thu\u1ed9c bi\u1ebfn.<\/td>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 12px 14px; border: 1px solid #cbd5e0;\">Th\u00e0nh th\u1ea1o c\u00e1c ph\u01b0\u01a1ng ph\u00e1p ph\u00e2n t\u00edch nh\u00e2n t\u1eed, gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh t\u00edch v\u00e0 ch\u1ee9ng minh bi\u1ec3u th\u1ee9c.<\/td>\n<\/tr>\n<tr>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 12px 14px; border: 1px solid #cbd5e0; font-weight: bold;\">Ng\u00e0y 5<\/td>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 12px 14px; border: 1px solid #cbd5e0;\">T\u1ee9 gi\u00e1c, h\u00ecnh thang c\u00e2n, h\u00ecnh b\u00ecnh h\u00e0nh, h\u00ecnh ch\u1eef nh\u1eadt, h\u00ecnh thoi, h\u00ecnh vu\u00f4ng.<\/td>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 12px 14px; border: 1px solid #cbd5e0;\">H\u1ec7 th\u1ed1ng h\u00f3a \u0111\u1ecbnh ngh\u0129a, t\u00ednh ch\u1ea5t v\u00e0 c\u00e1c d\u1ea5u hi\u1ec7u nh\u1eadn bi\u1ebft c\u00e1c h\u00ecnh \u0111\u1eb7c bi\u1ec7t trong h\u00ecnh h\u1ecdc ph\u1eb3ng.<\/td>\n<\/tr>\n<tr>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 12px 14px; border: 1px solid #cbd5e0; font-weight: bold;\">Ng\u00e0y 6<\/td>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 12px 14px; border: 1px solid #cbd5e0;\">L\u00e0m 2 \u0111\u1ec1 m\u1eabu b\u1ea5m gi\u1edd 90 ph\u00fat.<\/td>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 12px 14px; border: 1px solid #cbd5e0;\">L\u00e0m quen \u00e1p l\u1ef1c ph\u00f2ng thi th\u1eadt, r\u00e8n luy\u1ec7n k\u1ef9 n\u0103ng ph\u00e2n b\u1ed5 th\u1eddi gian h\u1ee3p l\u00fd gi\u1eefa tr\u1eafc nghi\u1ec7m v\u00e0 t\u1ef1 lu\u1eadn.<\/td>\n<\/tr>\n<tr>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 12px 14px; border: 1px solid #cbd5e0; font-weight: bold;\">Ng\u00e0y 7<\/td>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 12px 14px; border: 1px solid #cbd5e0;\">Xem l\u1ea1i l\u1ed7i sai, ngh\u1ec9 ng\u01a1i.<\/td>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 12px 14px; border: 1px solid #cbd5e0;\">Kh\u1eafc ph\u1ee5c tri\u1ec7t \u0111\u1ec3 c\u00e1c l\u1ed7i h\u1ed5ng ki\u1ebfn th\u1ee9c, \u00f4n l\u1ea1i l\u00fd thuy\u1ebft c\u1ed1t l\u00f5i v\u00e0 gi\u1eef t\u00e2m l\u00fd tho\u1ea3i m\u00e1i tr\u01b0\u1edbc ng\u00e0y thi.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p><!-- H\u1ed8P G\u1ee2I \u00dd \/ BLOG LINK --><\/p>\n<div style=\"background-color: #edf2f7; border-left: 4px solid #0056b3; padding: 14px 18px; border-radius: 4px; margin: 20px 0;\">\n<p style=\"margin: 0 0 10px 0; font-size: 15px; color: #2d3748;\"><strong>\ud83d\udca1 L\u1eddi khuy\u00ean cho h\u1ecdc sinh THCS:<\/strong> Giai \u0111o\u1ea1n h\u1ecdc t\u1eadp l\u1edbp 8 \u0111\u00f2i h\u1ecfi ph\u01b0\u01a1ng ph\u00e1p t\u1ef1 h\u1ecdc khoa h\u1ecdc v\u00e0 h\u1ec7 th\u1ed1ng h\u00f3a ki\u1ebfn th\u1ee9c ch\u1eb7t ch\u1ebd. Ba m\u1eb9 v\u00e0 h\u1ecdc sinh c\u00f3 th\u1ec3 tham kh\u1ea3o th\u00eam c\u00e1c ph\u01b0\u01a1ng ph\u00e1p <a style=\"color: #0056b3; font-weight: bold; text-decoration: underline;\" href=\"https:\/\/navi.edu.vn\/blog\/cach-hoc-toan-hieu-qua-thu-tu-hoc-chuan\/\">c\u00e1ch h\u1ecdc To\u00e1n hi\u1ec7u qu\u1ea3<\/a> \u0111\u1ec3 t\u1ed1i \u01b0u h\u00f3a n\u0103ng l\u1ef1c ti\u1ebfp thu m\u1ed7i ng\u00e0y.<\/p>\n<p style=\"margin: 0; font-size: 15px; color: #2d3748;\">B\u00ean c\u1ea1nh \u0111\u00f3, v\u00ec l\u1edbp 8 l\u00e0 b\u01b0\u1edbc \u0111\u1ec7m tr\u1ef1c ti\u1ebfp cho k\u1ef3 thi tuy\u1ec3n sinh v\u00e0o l\u1edbp 10, ba m\u1eb9 c\u00f3 th\u1ec3 xem tr\u01b0\u1edbc <a style=\"color: #0056b3; font-weight: bold; text-decoration: underline;\" href=\"https:\/\/navi.edu.vn\/blog\/de-cuong-on-tap-giua-ky-1-toan-9-2026-2027\/\">\u0111\u1ec1 c\u01b0\u01a1ng \u00f4n t\u1eadp gi\u1eefa k\u00ec 1 To\u00e1n 9<\/a> nh\u1eb1m chu\u1ea9n b\u1ecb s\u1edbm v\u00e0 \u0111\u1ecbnh h\u00ecnh l\u1ed9 tr\u00ecnh v\u1eefng ch\u1eafc cho n\u0103m h\u1ecdc cu\u1ed1i c\u1ea5p s\u1eafp t\u1edbi!<\/p>\n<\/div>\n<p><!-- CH\u1ee6 \u0110\u1ec0 2: T\u1ea2I \u0110\u1ec0 C\u01af\u01a0NG V\u00c0 \u0110\u1ec0 THI M\u1eaaU --><\/p>\n<h2 id=\"muc-18-tai-de-cuong-on-tap-giua-ki-1-toan-8-va-de-thi-mau-pdf-co-da\" style=\"color: #0056b3; border-bottom: 2px solid #e2e8f0; padding-bottom: 8px; margin-top: 35px; font-size: 20px;\">T\u1ea3i \u0111\u1ec1 c\u01b0\u01a1ng \u00f4n t\u1eadp gi\u1eefa k\u00ec 1 To\u00e1n 8 v\u00e0 \u0111\u1ec1 thi m\u1eabu (PDF c\u00f3 \u0111\u00e1p \u00e1n)<\/h2>\n<p>Nh\u1eb1m gi\u00fap h\u1ecdc sinh l\u1edbp 8 c\u1ecd x\u00e1t v\u1edbi c\u1ea5u tr\u00fac \u0111\u1ec1 ki\u1ec3m tra \u0111\u1ecbnh k\u00ec chu\u1ea9n m\u1ef1c theo Th\u00f4ng t\u01b0 22, \u0111\u1ed9i ng\u0169 gi\u00e1o vi\u00ean chuy\u00ean m\u00f4n t\u1ea1i NaviEdu \u0111\u00e3 bi\u00ean so\u1ea1n tr\u1ecdn b\u1ed9 t\u00e0i li\u1ec7u \u0111\u1ed9c quy\u1ec1n:<\/p>\n<div style=\"background-color: #f7fafc; border: 1px solid #e2e8f0; border-radius: 8px; padding: 22px; margin: 20px 0;\">\n<h3 style=\"color: #2b6cb0; font-size: 17px; margin-top: 0; margin-bottom: 12px;\">T\u00f3m t\u1eaft c\u1ea5u tr\u00fac b\u1ed9 \u0111\u1ec1 m\u1eabu NaviEdu:<\/h3>\n<ul style=\"padding-left: 20px; margin-bottom: 15px;\">\n<li><strong>Ph\u1ea7n Tr\u1eafc nghi\u1ec7m (3.0 \u0111i\u1ec3m):<\/strong> G\u1ed3m 12 c\u00e2u h\u1ecfi kh\u00e1ch quan (nhi\u1ec1u l\u1ef1a ch\u1ecdn), ki\u1ec3m tra nhanh nh\u1eadn bi\u1ebft v\u00e0 th\u00f4ng hi\u1ec3u to\u00e0n b\u1ed9 chuy\u00ean \u0111\u1ec1 \u0111a th\u1ee9c, h\u1eb1ng \u0111\u1eb3ng th\u1ee9c v\u00e0 t\u1ee9 gi\u00e1c.<\/li>\n<li><strong>Ph\u1ea7n T\u1ef1 lu\u1eadn (7.0 \u0111i\u1ec3m):<\/strong> \u0110\u01b0\u1ee3c chia th\u00e0nh c\u00e1c b\u00e0i c\u1ee5 th\u1ec3:\n<ul>\n<li><em>B\u00e0i 1 (1.5 \u0111i\u1ec3m):<\/em> Th\u1ef1c hi\u1ec7n ph\u00e9p t\u00ednh c\u1ed9ng, tr\u1eeb, nh\u00e2n \u0111a th\u1ee9c v\u00e0 chia \u0111a th\u1ee9c cho \u0111\u01a1n th\u1ee9c.<\/li>\n<li><em>B\u00e0i 2 (2.0 \u0111i\u1ec3m):<\/em> Ph\u00e2n t\u00edch \u0111a th\u1ee9c th\u00e0nh nh\u00e2n t\u1eed, t\u00ecm x v\u00e0 ch\u1ee9ng minh bi\u1ec3u th\u1ee9c kh\u00f4ng ph\u1ee5 thu\u1ed9c v\u00e0o bi\u1ebfn.<\/li>\n<li><em>B\u00e0i 3 (1.0 \u0111i\u1ec3m):<\/em> T\u00ednh s\u1ed1 \u0111o g\u00f3c trong t\u1ee9 gi\u00e1c v\u00e0 c\u00e1c b\u00e0i to\u00e1n t\u00ednh ch\u1ea5t \u0111o\u1ea1n th\u1eb3ng \u1edf h\u00ecnh thang c\u00e2n, h\u00ecnh b\u00ecnh h\u00e0nh.<\/li>\n<li><em>B\u00e0i 4 (2.0 \u0111i\u1ec3m):<\/em> B\u00e0i to\u00e1n h\u00ecnh h\u1ecdc ch\u1ee9ng minh t\u1ee9 gi\u00e1c l\u00e0 h\u00ecnh ch\u1eef nh\u1eadt, h\u00ecnh thoi ho\u1eb7c h\u00ecnh vu\u00f4ng, k\u1ebft h\u1ee3p t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng trung tuy\u1ebfn trong tam gi\u00e1c vu\u00f4ng.<\/li>\n<li><em>B\u00e0i 5 (0.5 \u0111i\u1ec3m &#8211; V\u1eadn d\u1ee5ng cao):<\/em> B\u00e0i to\u00e1n n\u00e2ng cao, t\u00ecm gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t, nh\u1ecf nh\u1ea5t c\u1ee7a bi\u1ec3u th\u1ee9c \u0111\u1ea1i s\u1ed1.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p style=\"margin-top: 15px; margin-bottom: 20px; color: #4a5568;\">To\u00e0n b\u1ed9 t\u00e0i li\u1ec7u bao g\u1ed3m t\u00f3m t\u1eaft l\u00fd thuy\u1ebft tr\u1ecdng t\u00e2m, h\u1ec7 th\u1ed1ng b\u00e0i t\u1eadp t\u1ef1 luy\u1ec7n theo t\u1eebng chuy\u00ean \u0111\u1ec1 v\u00e0 03 \u0111\u1ec1 thi th\u1eed chu\u1ea9n format 90 ph\u00fat c\u00f3 k\u00e8m b\u1ea3ng \u0111\u00e1p \u00e1n, h\u01b0\u1edbng d\u1eabn gi\u1ea3i chi ti\u1ebft t\u1eebng b\u01b0\u1edbc gi\u00fap con t\u1ef1 h\u1ecdc hi\u1ec7u qu\u1ea3 t\u1ea1i nh\u00e0:<\/p>\n<div style=\"text-align: center; margin-top: 25px; padding-top: 18px; border-top: 1px dashed #cbd5e0;\"><a style=\"background-color: #d9534f; color: #ffffff; padding: 13px 30px; text-decoration: none; border-radius: 6px; font-weight: bold; font-size: 16px; display: inline-block; box-shadow: 0 2px 5px rgba(217,83,79,0.3);\" href=\"https:\/\/navi.edu.vn\/thu-vien\/danh-muc-tai-lieu\/lop-8\/\">\ud83d\udce5 T\u1ea2I TR\u1eccN B\u1ed8 \u0110\u1ec0 C\u01af\u01a0NG &amp; \u0110\u1ec0 M\u1eaaU TO\u00c1N 8 (PDF)<br \/>\n<\/a><\/p>\n<p style=\"margin-top: 12px; font-size: 14px; color: #4a5568;\">(T\u00e0i li\u1ec7u \u0111\u01b0\u1ee3c c\u1eadp nh\u1eadt mi\u1ec5n ph\u00ed t\u1ea1i kho <a style=\"color: #0056b3; font-weight: bold; text-decoration: underline;\" href=\"https:\/\/navi.edu.vn\/thu-vien\/danh-muc-tai-lieu\/lop-8\/\">th\u01b0 vi\u1ec7n h\u1ecdc li\u1ec7u NaviEdu<\/a>)<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p><!-- K\u1ebeT TH\u00daC PH\u1ea6N III: L\u1ecaCH \u00d4N T\u1eacP 7 NG\u00c0Y & \u0110\u1ec0 THI M\u1eaaU TO\u00c1N 8 --><\/p>\n<p><!-- B\u1eaeT \u0110\u1ea6U K\u1ebeT B\u00c0I V\u00c0 KH\u1ed0I CTA WORDPRESS TO\u00c1N 8 --><\/p>\n<div class=\"naviedu-content-section\" style=\"font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif; line-height: 1.8; color: #2d3748; font-size: 16px;\">\n<h2 id=\"muc-19-loi-ket\" style=\"color: #0056b3; border-bottom: 2px solid #e2e8f0; padding-bottom: 8px; margin-top: 35px; font-size: 20px;\">L\u1eddi k\u1ebft<\/h2>\n<p>B\u01b0\u1edbc v\u00e0o ch\u01b0\u01a1ng tr\u00ecnh To\u00e1n 8 v\u1edbi nh\u1eefng chuy\u00ean \u0111\u1ec1 \u0111\u1ea1i s\u1ed1 n\u00e2ng cao v\u00e0 h\u00ecnh h\u1ecdc t\u1ee9 gi\u00e1c \u0111\u00f2i h\u1ecfi c\u00e1c em h\u1ecdc sinh s\u1ef1 ki\u00ean tr\u00ec, t\u01b0 duy logic s\u1eafc b\u00e9n c\u00f9ng ph\u01b0\u01a1ng ph\u00e1p \u00f4n luy\u1ec7n b\u00e0i b\u1ea3n. Vi\u1ec7c ch\u1ee7 \u0111\u1ed9ng h\u1ec7 th\u1ed1ng h\u00f3a ki\u1ebfn th\u1ee9c v\u00e0 luy\u1ec7n gi\u1ea3i c\u00e1c d\u1ea1ng b\u00e0i tr\u1ecdng t\u00e2m ch\u00ednh l\u00e0 ch\u00eca kh\u00f3a v\u00e0ng gi\u00fap c\u00e1c em t\u1ef1 tin b\u01b0\u1edbc v\u00e0o ph\u00f2ng thi.<\/p>\n<p>Hy v\u1ecdng r\u1eb1ng b\u1ed9 <strong>\u0111\u1ec1 c\u01b0\u01a1ng \u00f4n t\u1eadp gi\u1eefa k\u00ec 1 To\u00e1n 8<\/strong> do \u0111\u1ed9i ng\u0169 chuy\u00ean m\u00f4n NaviEdu bi\u00ean so\u1ea1n s\u1ebd l\u00e0 ng\u01b0\u1eddi b\u1ea1n \u0111\u1ed3ng h\u00e0nh tin c\u1eady, gi\u00fap ba m\u1eb9 v\u00e0 c\u00e1c con g\u1ee1 r\u1ed1i m\u1ecdi kh\u00f3 kh\u0103n. Ch\u00fac c\u00e1c em gi\u1eef v\u1eefng tinh th\u1ea7n t\u1eadp trung cao \u0111\u1ed9, \u00f4n t\u1eadp th\u00f4ng minh v\u00e0 gi\u00e0nh tr\u1ecdn \u0111i\u1ec3m s\u1ed1 th\u1eadt xu\u1ea5t s\u1eafc trong k\u00ec thi s\u1eafp t\u1edbi!<\/p>\n<p><!-- KH\u1ed0I CTA WORDPRESS CHU\u1ea8N CHUY\u1ec2N \u0110\u1ed4I --><\/p>\n<div style=\"border: 2px dashed #0056b3; background-color: #f4f8ff; border-radius: 10px; padding: 25px; text-align: center; margin: 35px 0;\">\n<h3 style=\"color: #0056b3; margin-top: 0; font-size: 20px; font-weight: bold;\">B\u1ee9t Ph\u00e1 \u0110i\u1ec3m S\u1ed1 Gi\u1eefa K\u00ec 1 To\u00e1n 8 C\u00f9ng L\u1ed9 Tr\u00ecnh C\u00e1 Nh\u00e2n H\u00f3a T\u1ea1i NaviEdu!<\/h3>\n<p style=\"font-size: 16px; line-height: 1.6; color: #333333; margin-bottom: 20px; max-width: 750px; margin-left: auto; margin-right: auto;\">Ba m\u1eb9 h\u00e3y \u0111\u01b0a con \u0111\u1ebfn c\u01a1 s\u1edf <strong>NaviEdu (33 LK6B M\u1ed7 Lao, L\u00e0ng Vi\u1ec7t Ki\u1ec1u Ch\u00e2u \u00c2u, H\u00e0 \u0110\u00f4ng)<\/strong> \u0111\u1ec3 tham gia l\u00e0m b\u00e0i \u0111\u00e1nh gi\u00e1 n\u0103ng l\u1ef1c mi\u1ec5n ph\u00ed b\u1eb1ng Math AI v\u00e0 nh\u1eadn l\u1ed9 tr\u00ecnh h\u1ecdc &#8220;may \u0111o&#8221; ri\u00eang bi\u1ec7t cho ch\u00ednh con ngay h\u00f4m nay!<\/p>\n<div><a style=\"background-color: #0056b3; color: #ffffff; padding: 13px 30px; text-decoration: none; border-radius: 6px; font-weight: bold; font-size: 16px; display: inline-block; box-shadow: 0 2px 4px rgba(0,86,179,0.2);\" href=\"https:\/\/navi.edu.vn\/giai-phap\/dang-ky-tu-van?utm_campaign=All.Blog._Organic.Dieuttm_Testtoan8.cta.2610_._.&amp;utm_medium=Dieuttm\" target=\"_blank\" rel=\"noopener\">L\u00c0M B\u00c0I \u0110\u00c1NH GI\u00c1 N\u0102NG L\u1ef0C MI\u1ec4N PH\u00cd<\/a><\/div>\n<\/div>\n<\/div>\n<p><!-- K\u1ebeT TH\u00daC K\u1ebeT B\u00c0I V\u00c0 KH\u1ed0I CTA WORDPRESS TO\u00c1N 8 --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0110\u1ec1 c\u01b0\u01a1ng \u00f4n t\u1eadp gi\u1eefa k\u00ec 1 To\u00e1n 8 (2026\u20132027): ki\u1ebfn th\u1ee9c tr\u1ecdng t\u00e2m, d\u1ea1ng b\u00e0i hay g\u1eb7p, \u0111\u1ec1 m\u1eabu c\u00f3 \u0111\u00e1p \u00e1n, l\u1ecbch \u00f4n 7 ng\u00e0y v\u00e0 file PDF t\u1ea3i mi\u1ec5n ph\u00ed.<\/p>\n","protected":false},"author":2,"featured_media":2905,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"categories":[6],"tags":[],"_links":{"self":[{"href":"https:\/\/navi.edu.vn\/blog\/wp-json\/wp\/v2\/posts\/2878"}],"collection":[{"href":"https:\/\/navi.edu.vn\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/navi.edu.vn\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/navi.edu.vn\/blog\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/navi.edu.vn\/blog\/wp-json\/wp\/v2\/comments?post=2878"}],"version-history":[{"count":5,"href":"https:\/\/navi.edu.vn\/blog\/wp-json\/wp\/v2\/posts\/2878\/revisions"}],"predecessor-version":[{"id":2907,"href":"https:\/\/navi.edu.vn\/blog\/wp-json\/wp\/v2\/posts\/2878\/revisions\/2907"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/navi.edu.vn\/blog\/wp-json\/wp\/v2\/media\/2905"}],"wp:attachment":[{"href":"https:\/\/navi.edu.vn\/blog\/wp-json\/wp\/v2\/media?parent=2878"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/navi.edu.vn\/blog\/wp-json\/wp\/v2\/categories?post=2878"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/navi.edu.vn\/blog\/wp-json\/wp\/v2\/tags?post=2878"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}