{"id":567199,"date":"2026-07-22T15:00:53","date_gmt":"2026-07-22T08:00:53","guid":{"rendered":"https:\/\/hoanghamobile.com\/tin-tuc\/?p=567199"},"modified":"2026-07-22T15:00:53","modified_gmt":"2026-07-22T08:00:53","slug":"nhi-thuc-newton","status":"publish","type":"post","link":"https:\/\/hoanghamobile.com\/tin-tuc\/nhi-thuc-newton\/","title":{"rendered":"Nh\u1ecb th\u1ee9c Newton: c\u00f4ng th\u1ee9c khai tri\u1ec3n v\u00e0 v\u00ed d\u1ee5"},"content":{"rendered":"<p>Nh\u1ecb th\u1ee9c Newton l\u00e0 c\u00f4ng th\u1ee9c khai tri\u1ec3n l\u0169y th\u1eeba c\u1ee7a m\u1ed9t t\u1ed5ng hai s\u1ed1 h\u1ea1ng, vi\u1ebft d\u01b0\u1edbi d\u1ea1ng (a + b)\u207f = \u03a3 C(n, k)\u00b7a\u207f\u207b\u1d4f\u00b7b\u1d4f v\u1edbi k ch\u1ea1y t\u1eeb 0 \u0111\u1ebfn n. Nh\u1edd c\u00f4ng th\u1ee9c n\u00e0y, b\u1ea1n c\u00f3 th\u1ec3 vi\u1ebft ngay k\u1ebft qu\u1ea3 khai tri\u1ec3n m\u00e0 kh\u00f4ng c\u1ea7n nh\u00e2n bi\u1ec3u th\u1ee9c nhi\u1ec1u l\u1ea7n. \u0110\u00e2y l\u00e0 n\u1ed9i dung tr\u1ecdng t\u00e2m trong ch\u01b0\u01a1ng tr\u00ecnh \u0110\u1ea1i s\u1ed1 \u2013 Gi\u1ea3i t\u00edch l\u1edbp 10, \u0111\u1ed3ng th\u1eddi l\u00e0 n\u1ec1n t\u1ea3ng cho t\u1ed5 h\u1ee3p, x\u00e1c su\u1ea5t \u1edf c\u00e1c l\u1edbp tr\u00ean. N\u1ed9i dung d\u01b0\u1edbi \u0111\u00e2y gi\u00fap b\u1ea1n n\u1eafm ch\u1eafc c\u00f4ng th\u1ee9c, s\u1ed1 h\u1ea1ng t\u1ed5ng qu\u00e1t, tam gi\u00e1c Pascal, c\u00e1c t\u00ednh ch\u1ea5t quan tr\u1ecdng v\u00e0 m\u1ed9t lo\u1ea1t v\u00ed d\u1ee5, b\u00e0i t\u1eadp c\u00f3 l\u1eddi gi\u1ea3i t\u1eebng b\u01b0\u1edbc \u0111\u1ec3 luy\u1ec7n t\u1eadp.<\/p>\n<h2>Nh\u1ecb th\u1ee9c Newton l\u00e0 g\u00ec?<\/h2>\n<p>Nh\u1ecb th\u1ee9c Newton (hay c\u00f4ng th\u1ee9c nh\u1ecb th\u1ee9c Newton) l\u00e0 c\u00f4ng th\u1ee9c cho ph\u00e9p khai tri\u1ec3n bi\u1ec3u th\u1ee9c (a + b)\u207f th\u00e0nh t\u1ed5ng c\u1ee7a nhi\u1ec1u s\u1ed1 h\u1ea1ng, v\u1edbi n l\u00e0 s\u1ed1 t\u1ef1 nhi\u00ean. Thay v\u00ec nh\u00e2n (a + b) v\u1edbi ch\u00ednh n\u00f3 n l\u1ea7n, b\u1ea1n ch\u1ec9 c\u1ea7n \u00e1p d\u1ee5ng c\u00f4ng th\u1ee9c \u0111\u1ec3 vi\u1ebft ra to\u00e0n b\u1ed9 c\u00e1c s\u1ed1 h\u1ea1ng theo m\u1ed9t quy lu\u1eadt c\u1ed1 \u0111\u1ecbnh. T\u00ean g\u1ecdi n\u00e0y g\u1eafn v\u1edbi nh\u00e0 to\u00e1n h\u1ecdc Isaac Newton, ng\u01b0\u1eddi \u0111\u00e3 t\u1ed5ng qu\u00e1t h\u00f3a c\u00f4ng th\u1ee9c khai tri\u1ec3n cho s\u1ed1 m\u0169 b\u1ea5t k\u1ef3.<\/p>\n<p><img fetchpriority=\"high\" decoding=\"async\" class=\"size-full wp-image-568951 aligncenter\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/nhi-thuc-newton-1.jpg\" alt=\"nhi-thuc-newton-1\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/nhi-thuc-newton-1.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/nhi-thuc-newton-1-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/nhi-thuc-newton-1-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<h2>C\u00f4ng th\u1ee9c nh\u1ecb th\u1ee9c Newton<\/h2>\n<p>V\u1edbi hai s\u1ed1 a, b v\u00e0 s\u1ed1 t\u1ef1 nhi\u00ean n, c\u00f4ng th\u1ee9c nh\u1ecb th\u1ee9c Newton \u0111\u01b0\u1ee3c vi\u1ebft nh\u01b0 sau:<\/p>\n<p>(a + b)\u207f = C(n,0)\u00b7a\u207f + C(n,1)\u00b7a\u207f\u207b\u00b9\u00b7b + C(n,2)\u00b7a\u207f\u207b\u00b2\u00b7b\u00b2 + \u2026 + C(n,n)\u00b7b\u207f<\/p>\n<p>Vi\u1ebft g\u1ecdn b\u1eb1ng k\u00fd hi\u1ec7u t\u1ed5ng: (a + b)\u207f = \u03a3<sub>k=0<\/sub><sup>n<\/sup> C(n, k)\u00b7a\u207f\u207b\u1d4f\u00b7b\u1d4f. Trong \u0111\u00f3 C(n, k) l\u00e0 s\u1ed1 t\u1ed5 h\u1ee3p ch\u1eadp k c\u1ee7a n, t\u00ednh theo c\u00f4ng th\u1ee9c C(n, k) = n! \/ [k!\u00b7(n \u2212 k)!], c\u00f2n g\u1ecdi l\u00e0 h\u1ec7 s\u1ed1 nh\u1ecb th\u1ee9c. Khai tri\u1ec3n lu\u00f4n c\u00f3 \u0111\u00fang n + 1 s\u1ed1 h\u1ea1ng: s\u1ed1 m\u0169 c\u1ee7a a gi\u1ea3m d\u1ea7n t\u1eeb n v\u1ec1 0, trong khi s\u1ed1 m\u0169 c\u1ee7a b t\u0103ng d\u1ea7n t\u1eeb 0 \u0111\u1ebfn n, t\u1ed5ng hai s\u1ed1 m\u0169 trong m\u1ed7i s\u1ed1 h\u1ea1ng lu\u00f4n b\u1eb1ng n.<\/p>\n<p><img decoding=\"async\" class=\"size-full wp-image-568952 aligncenter\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/nhi-thuc-newton-2.jpg\" alt=\"nhi-thuc-newton-2\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/nhi-thuc-newton-2.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/nhi-thuc-newton-2-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/nhi-thuc-newton-2-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<h2>S\u1ed1 h\u1ea1ng t\u1ed5ng qu\u00e1t<\/h2>\n<p>S\u1ed1 h\u1ea1ng t\u1ed5ng qu\u00e1t, hay s\u1ed1 h\u1ea1ng th\u1ee9 k + 1, trong khai tri\u1ec3n (a + b)\u207f \u0111\u01b0\u1ee3c vi\u1ebft l\u00e0:<\/p>\n<p>T<sub>k+1<\/sub> = C(n, k)\u00b7a\u207f\u207b\u1d4f\u00b7b\u1d4f<\/p>\n<p>C\u00f4ng th\u1ee9c s\u1ed1 h\u1ea1ng t\u1ed5ng qu\u00e1t r\u1ea5t h\u1eefu \u00edch khi \u0111\u1ec1 b\u00e0i ch\u1ec9 y\u00eau c\u1ea7u t\u00ecm m\u1ed9t s\u1ed1 h\u1ea1ng c\u1ee5 th\u1ec3 (v\u00ed d\u1ee5 s\u1ed1 h\u1ea1ng th\u1ee9 5) ho\u1eb7c h\u1ec7 s\u1ed1 c\u1ee7a m\u1ed9t l\u0169y th\u1eeba cho tr\u01b0\u1edbc, m\u00e0 kh\u00f4ng c\u1ea7n khai tri\u1ec3n to\u00e0n b\u1ed9 bi\u1ec3u th\u1ee9c. B\u1ea1n ch\u1ec9 c\u1ea7n x\u00e1c \u0111\u1ecbnh \u0111\u00fang gi\u00e1 tr\u1ecb k t\u01b0\u01a1ng \u1ee9ng r\u1ed3i thay v\u00e0o c\u00f4ng th\u1ee9c l\u00e0 ra k\u1ebft qu\u1ea3.<\/p>\n<h2>Tam gi\u00e1c Pascal v\u00e0 c\u00e1c h\u1ec7 s\u1ed1<\/h2>\n<p>C\u00e1c h\u1ec7 s\u1ed1 C(n, k) trong khai tri\u1ec3n nh\u1ecb th\u1ee9c Newton c\u00f3 th\u1ec3 tra nhanh t\u1eeb tam gi\u00e1c Pascal, trong \u0111\u00f3 m\u1ed7i s\u1ed1 (tr\u1eeb s\u1ed1 1 \u1edf hai \u0111\u1ea7u m\u1ed7i h\u00e0ng) b\u1eb1ng t\u1ed5ng hai s\u1ed1 li\u1ec1n k\u1ec1 \u1edf h\u00e0ng ngay ph\u00eda tr\u00ean. B\u1ea3ng d\u01b0\u1edbi \u0111\u00e2y li\u1ec7t k\u00ea c\u00e1c h\u1ec7 s\u1ed1 t\u1eeb n = 0 \u0111\u1ebfn n = 6:<\/p>\n<table>\n<thead>\n<tr>\n<th>n<\/th>\n<th>C\u00e1c h\u1ec7 s\u1ed1<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>0<\/td>\n<td>1<\/td>\n<\/tr>\n<tr>\n<td>1<\/td>\n<td>1   1<\/td>\n<\/tr>\n<tr>\n<td>2<\/td>\n<td>1   2   1<\/td>\n<\/tr>\n<tr>\n<td>3<\/td>\n<td>1   3   3   1<\/td>\n<\/tr>\n<tr>\n<td>4<\/td>\n<td>1   4   6   4   1<\/td>\n<\/tr>\n<tr>\n<td>5<\/td>\n<td>1   5   10   10   5   1<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>V\u00ed d\u1ee5, h\u00e0ng n = 5 cho ngay c\u00e1c h\u1ec7 s\u1ed1 c\u1ee7a khai tri\u1ec3n (a + b)\u2075 l\u00e0 1, 5, 10, 10, 5, 1 m\u00e0 kh\u00f4ng c\u1ea7n t\u00ednh t\u1eebng C(5, k) theo c\u00f4ng th\u1ee9c giai th\u1eeba.<\/p>\n<h2>T\u00ednh ch\u1ea5t c\u1ee7a khai tri\u1ec3n nh\u1ecb th\u1ee9c Newton<\/h2>\n<p>Khai tri\u1ec3n (a + b)\u207f c\u00f3 m\u1ed9t s\u1ed1 t\u00ednh ch\u1ea5t quan tr\u1ecdng n\u00ean nh\u1edb khi l\u00e0m b\u00e0i t\u1eadp:<\/p>\n<ul>\n<li>Khai tri\u1ec3n c\u00f3 \u0111\u00fang n + 1 s\u1ed1 h\u1ea1ng, s\u1eafp x\u1ebfp theo s\u1ed1 m\u0169 gi\u1ea3m d\u1ea7n c\u1ee7a a v\u00e0 t\u0103ng d\u1ea7n c\u1ee7a b.<\/li>\n<li>Trong m\u1ed7i s\u1ed1 h\u1ea1ng, t\u1ed5ng s\u1ed1 m\u0169 c\u1ee7a a v\u00e0 b lu\u00f4n b\u1eb1ng n.<\/li>\n<li>C\u00e1c h\u1ec7 s\u1ed1 nh\u1ecb th\u1ee9c \u0111\u1ed1i x\u1ee9ng: C(n, k) = C(n, n \u2212 k), t\u01b0\u01a1ng \u1ee9ng v\u1edbi t\u00ednh \u0111\u1ed1i x\u1ee9ng c\u1ee7a tam gi\u00e1c Pascal.<\/li>\n<li>T\u1ed5ng t\u1ea5t c\u1ea3 c\u00e1c h\u1ec7 s\u1ed1 trong khai tri\u1ec3n b\u1eb1ng 2\u207f, c\u00f3 \u0111\u01b0\u1ee3c khi cho a = b = 1.<\/li>\n<li>N\u1ebfu cho a = 1, b = \u22121, t\u1ed5ng c\u00e1c h\u1ec7 s\u1ed1 mang d\u1ea5u \u0111an xen b\u1eb1ng 0 v\u1edbi m\u1ecdi n \u2265 1.<\/li>\n<\/ul>\n<p><img decoding=\"async\" class=\"size-full wp-image-568953 aligncenter\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/nhi-thuc-newton-3.jpg\" alt=\"nhi-thuc-newton-3\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/nhi-thuc-newton-3.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/nhi-thuc-newton-3-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/nhi-thuc-newton-3-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<h2>V\u00ed d\u1ee5 khai tri\u1ec3n nh\u1ecb th\u1ee9c Newton<\/h2>\n<p>Hai v\u00ed d\u1ee5 d\u01b0\u1edbi \u0111\u00e2y minh h\u1ecda c\u00e1ch \u00e1p d\u1ee5ng c\u00f4ng th\u1ee9c t\u1eebng b\u01b0\u1edbc, t\u1eeb vi\u1ec7c x\u00e1c \u0111\u1ecbnh h\u1ec7 s\u1ed1 C(n, k) \u0111\u1ebfn khi ra k\u1ebft qu\u1ea3 cu\u1ed1i c\u00f9ng.<\/p>\n<h3>V\u00ed d\u1ee5 1: Khai tri\u1ec3n (x + 2)\u2074<\/h3>\n<p>\u00c1p d\u1ee5ng c\u00f4ng th\u1ee9c v\u1edbi a = x, b = 2, n = 4, t\u00ednh t\u1eebng s\u1ed1 h\u1ea1ng theo k t\u1eeb 0 \u0111\u1ebfn 4:<\/p>\n<ul>\n<li>k = 0: C(4,0)\u00b7x\u2074\u00b72\u2070 = x\u2074<\/li>\n<li>k = 1: C(4,1)\u00b7x\u00b3\u00b72\u00b9 = 4\u00b7x\u00b3\u00b72 = 8x\u00b3<\/li>\n<li>k = 2: C(4,2)\u00b7x\u00b2\u00b72\u00b2 = 6\u00b7x\u00b2\u00b74 = 24x\u00b2<\/li>\n<li>k = 3: C(4,3)\u00b7x\u00b9\u00b72\u00b3 = 4\u00b7x\u00b78 = 32x<\/li>\n<li>k = 4: C(4,4)\u00b7x\u2070\u00b72\u2074 = 16<\/li>\n<\/ul>\n<p>C\u1ed9ng l\u1ea1i: (x + 2)\u2074 = x\u2074 + 8x\u00b3 + 24x\u00b2 + 32x + 16.<\/p>\n<h3>V\u00ed d\u1ee5 2: Khai tri\u1ec3n (x \u2212 1)\u2075<\/h3>\n<p>V\u1edbi a = x, b = \u22121, n = 5, d\u1ea5u c\u1ee7a c\u00e1c s\u1ed1 h\u1ea1ng \u0111an xen do b mang d\u1ea5u \u00e2m:<\/p>\n<ul>\n<li>k = 0: C(5,0)\u00b7x\u2075 = x\u2075<\/li>\n<li>k = 1: C(5,1)\u00b7x\u2074\u00b7(\u22121) = \u22125x\u2074<\/li>\n<li>k = 2: C(5,2)\u00b7x\u00b3\u00b7(\u22121)\u00b2 = 10x\u00b3<\/li>\n<li>k = 3: C(5,3)\u00b7x\u00b2\u00b7(\u22121)\u00b3 = \u221210x\u00b2<\/li>\n<li>k = 4: C(5,4)\u00b7x\u00b7(\u22121)\u2074 = 5x<\/li>\n<li>k = 5: C(5,5)\u00b7(\u22121)\u2075 = \u22121<\/li>\n<\/ul>\n<p>K\u1ebft qu\u1ea3: (x \u2212 1)\u2075 = x\u2075 \u2212 5x\u2074 + 10x\u00b3 \u2212 10x\u00b2 + 5x \u2212 1. \u0110\u00e2y c\u0169ng ch\u00ednh l\u00e0 c\u00e1c h\u1ec7 s\u1ed1 \u1edf h\u00e0ng n = 5 c\u1ee7a tam gi\u00e1c Pascal, ch\u1ec9 kh\u00e1c nhau \u1edf d\u1ea5u \u0111an xen.<\/p>\n<p><strong>Xem th\u00eam: <a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/cong-thuc-tinh-quang-duong\/\">C\u00f4ng Th\u1ee9c T\u00ednh Qu\u00e3ng \u0110\u01b0\u1eddng: C\u00e1ch T\u00ednh To\u00e1n L\u1edbp 5 &amp; V\u1eadt L\u00fd L\u1edbp 8<\/a><\/strong><\/p>\n<h2>B\u00e0i t\u1eadp v\u1eadn d\u1ee5ng c\u00f3 l\u1eddi gi\u1ea3i<\/h2>\n<ul>\n<li><strong>B\u00e0i 1:<\/strong> Khai tri\u1ec3n (x + 2)\u00b3. <em>L\u1eddi gi\u1ea3i:<\/em> V\u1edbi a = x, b = 2, n = 3: (x + 2)\u00b3 = C(3,0)x\u00b3 + C(3,1)x\u00b2\u00b72 + C(3,2)x\u00b72\u00b2 + C(3,3)\u00b72\u00b3 = x\u00b3 + 6x\u00b2 + 12x + 8.<\/li>\n<li><strong>B\u00e0i 2:<\/strong> T\u00ecm s\u1ed1 h\u1ea1ng th\u1ee9 3 trong khai tri\u1ec3n (a + b)\u2075. <em>L\u1eddi gi\u1ea3i:<\/em> S\u1ed1 h\u1ea1ng th\u1ee9 3 \u1ee9ng v\u1edbi k + 1 = 3 n\u00ean k = 2: T\u2083 = C(5,2)\u00b7a\u00b3\u00b7b\u00b2 = 10a\u00b3b\u00b2.<\/li>\n<li><strong>B\u00e0i 3:<\/strong> Khai tri\u1ec3n (2x \u2212 1)\u00b2 v\u00e0 cho bi\u1ebft c\u00f3 bao nhi\u00eau s\u1ed1 h\u1ea1ng. <em>L\u1eddi gi\u1ea3i:<\/em> n = 2 n\u00ean c\u00f3 n + 1 = 3 s\u1ed1 h\u1ea1ng: (2x \u2212 1)\u00b2 = (2x)\u00b2 \u2212 2\u00b72x\u00b71 + 1\u00b2 = 4x\u00b2 \u2212 4x + 1.<\/li>\n<li><strong>B\u00e0i 4:<\/strong> T\u00ednh t\u1ed5ng c\u00e1c h\u1ec7 s\u1ed1 trong khai tri\u1ec3n (x + 1)\u2076. <em>L\u1eddi gi\u1ea3i:<\/em> Cho x = 1, t\u1ed5ng h\u1ec7 s\u1ed1 b\u1eb1ng (1 + 1)\u2076 = 2\u2076 = 64.<\/li>\n<li><strong>B\u00e0i 5:<\/strong> T\u00ecm h\u1ec7 s\u1ed1 c\u1ee7a x\u00b2 trong khai tri\u1ec3n (x \u2212 3)\u2075. <em>L\u1eddi gi\u1ea3i:<\/em> S\u1ed1 h\u1ea1ng t\u1ed5ng qu\u00e1t T<sub>k+1<\/sub> = C(5,k)\u00b7x\u2075\u207b\u1d4f\u00b7(\u22123)\u1d4f. C\u1ea7n 5 \u2212 k = 2 n\u00ean k = 3. H\u1ec7 s\u1ed1 c\u1ea7n t\u00ecm l\u00e0 C(5,3)\u00b7(\u22123)\u00b3 = 10\u00b7(\u221227) = \u2212270.<\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-568954 aligncenter\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/nhi-thuc-newton-4.jpg\" alt=\"nhi-thuc-newton-4\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/nhi-thuc-newton-4.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/nhi-thuc-newton-4-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/nhi-thuc-newton-4-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<h2>C\u00e1ch t\u00ecm h\u1ec7 s\u1ed1 c\u1ee7a m\u1ed9t s\u1ed1 h\u1ea1ng c\u1ee5 th\u1ec3<\/h2>\n<p>M\u1ed9t d\u1ea1ng b\u00e0i th\u01b0\u1eddng g\u1eb7p l\u00e0 t\u00ecm h\u1ec7 s\u1ed1 c\u1ee7a s\u1ed1 h\u1ea1ng ch\u1ee9a m\u1ed9t l\u0169y th\u1eeba cho tr\u01b0\u1edbc m\u00e0 kh\u00f4ng c\u1ea7n khai tri\u1ec3n to\u00e0n b\u1ed9 bi\u1ec3u th\u1ee9c. C\u00e1ch th\u1ef1c hi\u1ec7n g\u1ed3m hai b\u01b0\u1edbc:<\/p>\n<ul>\n<li>Vi\u1ebft s\u1ed1 h\u1ea1ng t\u1ed5ng qu\u00e1t T<sub>k+1<\/sub> = C(n, k)\u00b7a\u207f\u207b\u1d4f\u00b7b\u1d4f.<\/li>\n<li>Cho s\u1ed1 m\u0169 c\u1ee7a bi\u1ebfn trong s\u1ed1 h\u1ea1ng t\u1ed5ng qu\u00e1t b\u1eb1ng l\u0169y th\u1eeba \u0111\u1ec1 b\u00e0i y\u00eau c\u1ea7u, gi\u1ea3i ra k, r\u1ed3i thay k v\u00e0o \u0111\u1ec3 t\u00ednh h\u1ec7 s\u1ed1.<\/li>\n<\/ul>\n<p>V\u00ed d\u1ee5, \u0111\u1ec3 t\u00ecm h\u1ec7 s\u1ed1 c\u1ee7a x\u00b3 trong khai tri\u1ec3n (x + 2)\u2075, s\u1ed1 h\u1ea1ng t\u1ed5ng qu\u00e1t l\u00e0 C(5, k)\u00b7x\u2075\u207b\u1d4f\u00b72\u1d4f. T\u1eeb 5 \u2212 k = 3 suy ra k = 2. H\u1ec7 s\u1ed1 c\u1ea7n t\u00ecm l\u00e0 C(5, 2)\u00b72\u00b2 = 10 \u00d7 4 = 40.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-568955 aligncenter\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/nhi-thuc-newton-5.jpg\" alt=\"nhi-thuc-newton-5\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/nhi-thuc-newton-5.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/nhi-thuc-newton-5-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/nhi-thuc-newton-5-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<h2>\u1ee8ng d\u1ee5ng c\u1ee7a nh\u1ecb th\u1ee9c Newton<\/h2>\n<p>Nh\u1ecb th\u1ee9c Newton kh\u00f4ng ch\u1ec9 d\u00f9ng \u0111\u1ec3 khai tri\u1ec3n l\u0169y th\u1eeba m\u00e0 c\u00f2n l\u00e0 c\u00f4ng c\u1ee5 n\u1ec1n t\u1ea3ng trong nhi\u1ec1u d\u1ea1ng to\u00e1n kh\u00e1c. C\u00f4ng th\u1ee9c gi\u00fap khai tri\u1ec3n nhanh c\u00e1c bi\u1ec3u th\u1ee9c b\u1eadc cao, t\u00ednh gi\u00e1 tr\u1ecb g\u1ea7n \u0111\u00fang, ch\u1ee9ng minh c\u00e1c \u0111\u1eb3ng th\u1ee9c t\u1ed5 h\u1ee3p v\u00e0 gi\u1ea3i c\u00e1c b\u00e0i to\u00e1n \u0111\u1ebfm, x\u00e1c su\u1ea5t. \u0110\u00e2y l\u00e0 ki\u1ebfn th\u1ee9c d\u00f9ng xuy\u00ean su\u1ed1t t\u1eeb ph\u1ed5 th\u00f4ng \u0111\u1ebfn \u0111\u1ea1i h\u1ecdc, \u0111\u1eb7c bi\u1ec7t \u1edf chuy\u00ean \u0111\u1ec1 t\u1ed5 h\u1ee3p \u2013 x\u00e1c su\u1ea5t.<\/p>\n<p><strong>Xem th\u00eam: <a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/phuong-trinh-luong-giac\/\">Ph\u01b0\u01a1ng tr\u00ecnh l\u01b0\u1ee3ng gi\u00e1c c\u01a1 b\u1ea3n: c\u00f4ng th\u1ee9c nghi\u1ec7m v\u00e0 v\u00ed d\u1ee5<\/a><\/strong><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-568956 aligncenter\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/nhi-thuc-newton-6.jpg\" alt=\"nhi-thuc-newton-6\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/nhi-thuc-newton-6.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/nhi-thuc-newton-6-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/nhi-thuc-newton-6-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<h2>C\u00e2u h\u1ecfi th\u01b0\u1eddng g\u1eb7p v\u1ec1 nh\u1ecb th\u1ee9c Newton<\/h2>\n<h3>Nh\u1ecb th\u1ee9c Newton l\u00e0 g\u00ec?<\/h3>\n<p>L\u00e0 c\u00f4ng th\u1ee9c khai tri\u1ec3n (a + b)\u207f th\u00e0nh t\u1ed5ng c\u00e1c s\u1ed1 h\u1ea1ng d\u1ea1ng C(n, k)\u00b7a\u207f\u207b\u1d4f\u00b7b\u1d4f, v\u1edbi k ch\u1ea1y t\u1eeb 0 \u0111\u1ebfn n.<\/p>\n<h3>Khai tri\u1ec3n (a + b)\u207f c\u00f3 bao nhi\u00eau s\u1ed1 h\u1ea1ng?<\/h3>\n<p>C\u00f3 \u0111\u00fang n + 1 s\u1ed1 h\u1ea1ng.<\/p>\n<h3>S\u1ed1 h\u1ea1ng t\u1ed5ng qu\u00e1t c\u1ee7a nh\u1ecb th\u1ee9c Newton l\u00e0 g\u00ec?<\/h3>\n<p>L\u00e0 T<sub>k+1<\/sub> = C(n, k)\u00b7a\u207f\u207b\u1d4f\u00b7b\u1d4f, d\u00f9ng \u0111\u1ec3 t\u00ecm nhanh m\u1ed9t s\u1ed1 h\u1ea1ng ho\u1eb7c h\u1ec7 s\u1ed1 b\u1ea5t k\u1ef3 m\u00e0 kh\u00f4ng c\u1ea7n khai tri\u1ec3n to\u00e0n b\u1ed9.<\/p>\n<h3>Tam gi\u00e1c Pascal d\u00f9ng \u0111\u1ec3 l\u00e0m g\u00ec?<\/h3>\n<p>D\u00f9ng \u0111\u1ec3 tra nhanh c\u00e1c h\u1ec7 s\u1ed1 nh\u1ecb th\u1ee9c C(n, k) m\u00e0 kh\u00f4ng c\u1ea7n t\u00ednh giai th\u1eeba t\u1eebng b\u01b0\u1edbc.<\/p>\n<h3>T\u1ed5ng c\u00e1c h\u1ec7 s\u1ed1 trong khai tri\u1ec3n (a + b)\u207f b\u1eb1ng bao nhi\u00eau?<\/h3>\n<p>B\u1eb1ng 2\u207f, c\u00f3 \u0111\u01b0\u1ee3c khi thay a = b = 1 v\u00e0o khai tri\u1ec3n.<\/p>\n<h3>C\u00f4ng th\u1ee9c t\u00ednh C(n, k) nh\u01b0 th\u1ebf n\u00e0o?<\/h3>\n<p>C(n, k) = n! \/ [k!\u00b7(n \u2212 k)!], trong \u0111\u00f3 n! l\u00e0 t\u00edch c\u00e1c s\u1ed1 t\u1ef1 nhi\u00ean li\u00ean ti\u1ebfp t\u1eeb 1 \u0111\u1ebfn n.<\/p>\n<h3>L\u00e0m sao \u0111\u1ec3 t\u00ecm h\u1ec7 s\u1ed1 c\u1ee7a m\u1ed9t s\u1ed1 h\u1ea1ng ch\u1ee9a x\u1d50 trong khai tri\u1ec3n?<\/h3>\n<p>Vi\u1ebft s\u1ed1 h\u1ea1ng t\u1ed5ng qu\u00e1t, cho s\u1ed1 m\u0169 c\u1ee7a x b\u1eb1ng m \u0111\u1ec3 t\u00ecm k, r\u1ed3i thay k v\u00e0o c\u00f4ng th\u1ee9c \u0111\u1ec3 t\u00ednh h\u1ec7 s\u1ed1 t\u01b0\u01a1ng \u1ee9ng.<\/p>\n<h2>K\u1ebft lu\u1eadn<\/h2>\n<p>T\u00f3m l\u1ea1i, nh\u1ecb th\u1ee9c Newton khai tri\u1ec3n (a + b)\u207f theo c\u00f4ng th\u1ee9c (a + b)\u207f = \u03a3 C(n, k)\u00b7a\u207f\u207b\u1d4f\u00b7b\u1d4f, lu\u00f4n g\u1ed3m n + 1 s\u1ed1 h\u1ea1ng v\u1edbi c\u00e1c h\u1ec7 s\u1ed1 l\u1ea5y t\u1eeb tam gi\u00e1c Pascal. N\u1eafm v\u1eefng s\u1ed1 h\u1ea1ng t\u1ed5ng qu\u00e1t T<sub>k+1<\/sub> s\u1ebd gi\u00fap b\u1ea1n x\u1eed l\u00fd nhanh c\u00e1c d\u1ea1ng b\u00e0i t\u00ecm s\u1ed1 h\u1ea1ng ho\u1eb7c h\u1ec7 s\u1ed1 m\u00e0 kh\u00f4ng c\u1ea7n khai tri\u1ec3n to\u00e0n b\u1ed9 bi\u1ec3u th\u1ee9c. \u0110\u1ec3 luy\u1ec7n th\u00eam, m\u1eddi b\u1ea1n tham kh\u1ea3o c\u00e1c b\u00e0i <strong><a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/cong-thuc-to-hop-chinh-hop\/\">c\u00f4ng th\u1ee9c t\u1ed5 h\u1ee3p, ch\u1ec9nh h\u1ee3p<\/a>, <a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/tap-hop-so-nguyen-z-la-gi-giai-ma-toan-dien-ve-z-trong-toan-hoc\/\">t\u1eadp h\u1ee3p s\u1ed1 nguy\u00ean Z l\u00e0 g\u00ec<\/a><\/strong> v\u00e0 <a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/1-nam-anh-sang-bang-bao-nhieu-km\/\"><strong>m\u1ed9t n\u0103m \u00e1nh s\u00e1ng b\u1eb1ng bao nhi\u00eau km<\/strong><\/a> tr\u00ean chuy\u00ean m\u1ee5c tin t\u1ee9c c\u1ee7a Ho\u00e0ng H\u00e0 Mobile.<\/p>\n<p><script type=\"application\/ld+json\">\n{\"@context\":\"https:\/\/schema.org\",\"@type\":\"FAQPage\",\"mainEntity\":[{\"@type\":\"Question\",\"name\":\"Nh\u1ecb th\u1ee9c Newton l\u00e0 g\u00ec?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"L\u00e0 c\u00f4ng th\u1ee9c khai tri\u1ec3n (a + b)^n th\u00e0nh t\u1ed5ng c\u00e1c s\u1ed1 h\u1ea1ng d\u1ea1ng C(n,k)\u00b7a^(n-k)\u00b7b^k, v\u1edbi k ch\u1ea1y t\u1eeb 0 \u0111\u1ebfn n.\"}},{\"@type\":\"Question\",\"name\":\"Khai tri\u1ec3n (a + b)^n c\u00f3 bao nhi\u00eau s\u1ed1 h\u1ea1ng?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"C\u00f3 \u0111\u00fang n + 1 s\u1ed1 h\u1ea1ng.\"}},{\"@type\":\"Question\",\"name\":\"S\u1ed1 h\u1ea1ng t\u1ed5ng qu\u00e1t c\u1ee7a nh\u1ecb th\u1ee9c Newton l\u00e0 g\u00ec?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"L\u00e0 T(k+1) = C(n,k)\u00b7a^(n-k)\u00b7b^k, d\u00f9ng \u0111\u1ec3 t\u00ecm nhanh m\u1ed9t s\u1ed1 h\u1ea1ng ho\u1eb7c h\u1ec7 s\u1ed1 b\u1ea5t k\u1ef3 m\u00e0 kh\u00f4ng c\u1ea7n khai tri\u1ec3n to\u00e0n b\u1ed9.\"}},{\"@type\":\"Question\",\"name\":\"Tam gi\u00e1c Pascal d\u00f9ng \u0111\u1ec3 l\u00e0m g\u00ec?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"D\u00f9ng \u0111\u1ec3 tra nhanh c\u00e1c h\u1ec7 s\u1ed1 nh\u1ecb th\u1ee9c C(n,k) m\u00e0 kh\u00f4ng c\u1ea7n t\u00ednh giai th\u1eeba t\u1eebng b\u01b0\u1edbc.\"}},{\"@type\":\"Question\",\"name\":\"T\u1ed5ng c\u00e1c h\u1ec7 s\u1ed1 trong khai tri\u1ec3n (a + b)^n b\u1eb1ng bao nhi\u00eau?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"B\u1eb1ng 2^n, c\u00f3 \u0111\u01b0\u1ee3c khi thay a = b = 1 v\u00e0o khai tri\u1ec3n.\"}},{\"@type\":\"Question\",\"name\":\"C\u00f4ng th\u1ee9c t\u00ednh C(n,k) nh\u01b0 th\u1ebf n\u00e0o?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"C(n,k) = n! \/ (k!\u00b7(n-k)!), trong \u0111\u00f3 n! l\u00e0 t\u00edch c\u00e1c s\u1ed1 t\u1ef1 nhi\u00ean li\u00ean ti\u1ebfp t\u1eeb 1 \u0111\u1ebfn n.\"}},{\"@type\":\"Question\",\"name\":\"L\u00e0m sao \u0111\u1ec3 t\u00ecm h\u1ec7 s\u1ed1 c\u1ee7a m\u1ed9t s\u1ed1 h\u1ea1ng ch\u1ee9a x^m trong khai tri\u1ec3n?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Vi\u1ebft s\u1ed1 h\u1ea1ng t\u1ed5ng qu\u00e1t, cho s\u1ed1 m\u0169 c\u1ee7a x b\u1eb1ng m \u0111\u1ec3 t\u00ecm k, r\u1ed3i thay k v\u00e0o c\u00f4ng th\u1ee9c \u0111\u1ec3 t\u00ednh h\u1ec7 s\u1ed1 t\u01b0\u01a1ng \u1ee9ng.\"}}]}\n<\/script><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Nh\u1ecb th\u1ee9c Newton l\u00e0 c\u00f4ng th\u1ee9c khai tri\u1ec3n l\u0169y th\u1eeba c\u1ee7a m\u1ed9t t\u1ed5ng hai s\u1ed1 h\u1ea1ng, vi\u1ebft d\u01b0\u1edbi d\u1ea1ng (a + b)\u207f = \u03a3 C(n, k)\u00b7a\u207f\u207b\u1d4f\u00b7b\u1d4f v\u1edbi k ch\u1ea1y t\u1eeb 0 \u0111\u1ebfn n. Nh\u1edd c\u00f4ng th\u1ee9c n\u00e0y, b\u1ea1n c\u00f3 th\u1ec3 vi\u1ebft ngay k\u1ebft qu\u1ea3 khai tri\u1ec3n m\u00e0 kh\u00f4ng c\u1ea7n nh\u00e2n bi\u1ec3u th\u1ee9c nhi\u1ec1u l\u1ea7n. \u0110\u00e2y [&hellip;]<\/p>\n","protected":false},"author":65,"featured_media":568950,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"nh\u1ecb th\u1ee9c newton","_yoast_wpseo_title":"Nh\u1ecb th\u1ee9c Newton: c\u00f4ng th\u1ee9c v\u00e0 v\u00ed d\u1ee5","_yoast_wpseo_metadesc":"Nh\u1ecb th\u1ee9c Newton l\u00e0 g\u00ec? C\u00f4ng th\u1ee9c khai tri\u1ec3n, s\u1ed1 h\u1ea1ng t\u1ed5ng qu\u00e1t, tam gi\u00e1c Pascal v\u00e0 b\u00e0i t\u1eadp c\u00f3 l\u1eddi gi\u1ea3i chi ti\u1ebft, d\u1ec5 hi\u1ec3u cho h\u1ecdc sinh l\u1edbp 10.","footnotes":""},"categories":[16],"tags":[],"class_list":["post-567199","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-thu-thuat"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v27.3 (Yoast SEO v27.4) - https:\/\/yoast.com\/product\/yoast-seo-premium-wordpress\/ -->\n<title>Nh\u1ecb th\u1ee9c Newton: c\u00f4ng th\u1ee9c v\u00e0 v\u00ed d\u1ee5<\/title>\n<meta name=\"description\" content=\"Nh\u1ecb th\u1ee9c Newton l\u00e0 g\u00ec? C\u00f4ng th\u1ee9c khai tri\u1ec3n, s\u1ed1 h\u1ea1ng t\u1ed5ng qu\u00e1t, tam gi\u00e1c Pascal v\u00e0 b\u00e0i t\u1eadp c\u00f3 l\u1eddi gi\u1ea3i chi ti\u1ebft, d\u1ec5 hi\u1ec3u cho h\u1ecdc sinh l\u1edbp 10.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/hoanghamobile.com\/tin-tuc\/nhi-thuc-newton\/\" \/>\n<meta property=\"og:locale\" content=\"vi_VN\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Nh\u1ecb th\u1ee9c Newton: c\u00f4ng th\u1ee9c khai tri\u1ec3n v\u00e0 v\u00ed d\u1ee5\" \/>\n<meta property=\"og:description\" content=\"Nh\u1ecb th\u1ee9c Newton l\u00e0 g\u00ec? C\u00f4ng th\u1ee9c khai tri\u1ec3n, s\u1ed1 h\u1ea1ng t\u1ed5ng qu\u00e1t, tam gi\u00e1c Pascal v\u00e0 b\u00e0i t\u1eadp c\u00f3 l\u1eddi gi\u1ea3i chi ti\u1ebft, d\u1ec5 hi\u1ec3u cho h\u1ecdc sinh l\u1edbp 10.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/hoanghamobile.com\/tin-tuc\/nhi-thuc-newton\/\" \/>\n<meta property=\"og:site_name\" content=\"Tin t\u1ee9c c\u00f4ng ngh\u1ec7 - HoangHaMobile\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/hoanghamobilecom\" \/>\n<meta property=\"article:author\" content=\"https:\/\/www.facebook.com\/hoanghamobilecom\" \/>\n<meta property=\"article:published_time\" content=\"2026-07-22T08:00:53+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/nhi-thuc-newton.jpg\" \/>\n\t<meta property=\"og:image:width\" content=\"1200\" \/>\n\t<meta property=\"og:image:height\" content=\"628\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/jpeg\" \/>\n<meta name=\"author\" content=\"Vo Giang\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"\u0110\u01b0\u1ee3c vi\u1ebft b\u1edfi\" \/>\n\t<meta name=\"twitter:data1\" content=\"Vo Giang\" \/>\n\t<meta name=\"twitter:label2\" content=\"\u01af\u1edbc t\u00ednh th\u1eddi gian \u0111\u1ecdc\" \/>\n\t<meta name=\"twitter:data2\" content=\"7 ph\u00fat\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\\\/\\\/hoanghamobile.com\\\/tin-tuc\\\/nhi-thuc-newton\\\/#article\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/hoanghamobile.com\\\/tin-tuc\\\/nhi-thuc-newton\\\/\"},\"author\":{\"name\":\"Vo Giang\",\"@id\":\"https:\\\/\\\/hoanghamobile.com\\\/tin-tuc\\\/#\\\/schema\\\/person\\\/72d0493d28396e6a0cdc358e9260c03c\"},\"headline\":\"Nh\u1ecb th\u1ee9c Newton: c\u00f4ng th\u1ee9c khai tri\u1ec3n v\u00e0 v\u00ed d\u1ee5\",\"datePublished\":\"2026-07-22T08:00:53+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\\\/\\\/hoanghamobile.com\\\/tin-tuc\\\/nhi-thuc-newton\\\/\"},\"wordCount\":2095,\"publisher\":{\"@id\":\"https:\\\/\\\/hoanghamobile.com\\\/tin-tuc\\\/#organization\"},\"image\":{\"@id\":\"https:\\\/\\\/hoanghamobile.com\\\/tin-tuc\\\/nhi-thuc-newton\\\/#primaryimage\"},\"thumbnailUrl\":\"https:\\\/\\\/hoanghamobile.com\\\/tin-tuc\\\/wp-content\\\/uploads\\\/2026\\\/07\\\/nhi-thuc-newton.jpg\",\"articleSection\":[\"Th\u1ee7 thu\u1eadt\"],\"inLanguage\":\"vi\",\"copyrightYear\":\"2026\",\"copyrightHolder\":{\"@id\":\"https:\\\/\\\/hoanghamobile.com\\\/tin-tuc\\\/#organization\"}},{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/hoanghamobile.com\\\/tin-tuc\\\/nhi-thuc-newton\\\/\",\"url\":\"https:\\\/\\\/hoanghamobile.com\\\/tin-tuc\\\/nhi-thuc-newton\\\/\",\"name\":\"Nh\u1ecb th\u1ee9c Newton: c\u00f4ng th\u1ee9c v\u00e0 v\u00ed d\u1ee5\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/hoanghamobile.com\\\/tin-tuc\\\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\\\/\\\/hoanghamobile.com\\\/tin-tuc\\\/nhi-thuc-newton\\\/#primaryimage\"},\"image\":{\"@id\":\"https:\\\/\\\/hoanghamobile.com\\\/tin-tuc\\\/nhi-thuc-newton\\\/#primaryimage\"},\"thumbnailUrl\":\"https:\\\/\\\/hoanghamobile.com\\\/tin-tuc\\\/wp-content\\\/uploads\\\/2026\\\/07\\\/nhi-thuc-newton.jpg\",\"datePublished\":\"2026-07-22T08:00:53+00:00\",\"description\":\"Nh\u1ecb th\u1ee9c Newton l\u00e0 g\u00ec? C\u00f4ng th\u1ee9c khai tri\u1ec3n, s\u1ed1 h\u1ea1ng t\u1ed5ng qu\u00e1t, tam gi\u00e1c Pascal v\u00e0 b\u00e0i t\u1eadp c\u00f3 l\u1eddi gi\u1ea3i chi ti\u1ebft, d\u1ec5 hi\u1ec3u cho h\u1ecdc sinh l\u1edbp 10.\",\"breadcrumb\":{\"@id\":\"https:\\\/\\\/hoanghamobile.com\\\/tin-tuc\\\/nhi-thuc-newton\\\/#breadcrumb\"},\"inLanguage\":\"vi\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\\\/\\\/hoanghamobile.com\\\/tin-tuc\\\/nhi-thuc-newton\\\/\"]}]},{\"@type\":\"ImageObject\",\"inLanguage\":\"vi\",\"@id\":\"https:\\\/\\\/hoanghamobile.com\\\/tin-tuc\\\/nhi-thuc-newton\\\/#primaryimage\",\"url\":\"https:\\\/\\\/hoanghamobile.com\\\/tin-tuc\\\/wp-content\\\/uploads\\\/2026\\\/07\\\/nhi-thuc-newton.jpg\",\"contentUrl\":\"https:\\\/\\\/hoanghamobile.com\\\/tin-tuc\\\/wp-content\\\/uploads\\\/2026\\\/07\\\/nhi-thuc-newton.jpg\",\"width\":1200,\"height\":628,\"caption\":\"nhi-thuc-newton\"},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\\\/\\\/hoanghamobile.com\\\/tin-tuc\\\/nhi-thuc-newton\\\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Trang ch\u1ee7\",\"item\":\"https:\\\/\\\/hoanghamobile.com\\\/tin-tuc\\\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Nh\u1ecb th\u1ee9c Newton: c\u00f4ng th\u1ee9c khai tri\u1ec3n v\u00e0 v\u00ed d\u1ee5\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\\\/\\\/hoanghamobile.com\\\/tin-tuc\\\/#website\",\"url\":\"https:\\\/\\\/hoanghamobile.com\\\/tin-tuc\\\/\",\"name\":\"Tin t\u1ee9c c\u00f4ng ngh\u1ec7 - HoangHaMobile\",\"description\":\"\",\"publisher\":{\"@id\":\"https:\\\/\\\/hoanghamobile.com\\\/tin-tuc\\\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\\\/\\\/hoanghamobile.com\\\/tin-tuc\\\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"vi\"},{\"@type\":\"Organization\",\"@id\":\"https:\\\/\\\/hoanghamobile.com\\\/tin-tuc\\\/#organization\",\"name\":\"Tin t\u1ee9c c\u00f4ng ngh\u1ec7 - HoangHaMobile\",\"url\":\"https:\\\/\\\/hoanghamobile.com\\\/tin-tuc\\\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"vi\",\"@id\":\"https:\\\/\\\/hoanghamobile.com\\\/tin-tuc\\\/#\\\/schema\\\/logo\\\/image\\\/\",\"url\":\"https:\\\/\\\/hoanghamobile.com\\\/tin-tuc\\\/wp-content\\\/uploads\\\/2021\\\/12\\\/logo-text.png\",\"contentUrl\":\"https:\\\/\\\/hoanghamobile.com\\\/tin-tuc\\\/wp-content\\\/uploads\\\/2021\\\/12\\\/logo-text.png\",\"width\":256,\"height\":37,\"caption\":\"Tin t\u1ee9c c\u00f4ng ngh\u1ec7 - HoangHaMobile\"},\"image\":{\"@id\":\"https:\\\/\\\/hoanghamobile.com\\\/tin-tuc\\\/#\\\/schema\\\/logo\\\/image\\\/\"},\"sameAs\":[\"https:\\\/\\\/www.facebook.com\\\/hoanghamobilecom\"]},{\"@type\":\"Person\",\"@id\":\"https:\\\/\\\/hoanghamobile.com\\\/tin-tuc\\\/#\\\/schema\\\/person\\\/72d0493d28396e6a0cdc358e9260c03c\",\"name\":\"Vo Giang\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"vi\",\"@id\":\"https:\\\/\\\/secure.gravatar.com\\\/avatar\\\/77997fb123ed6295d07f6612ad5a1afc8283a96f9c379981b21365a22e2cff35?s=96&d=mm&r=g\",\"url\":\"https:\\\/\\\/secure.gravatar.com\\\/avatar\\\/77997fb123ed6295d07f6612ad5a1afc8283a96f9c379981b21365a22e2cff35?s=96&d=mm&r=g\",\"contentUrl\":\"https:\\\/\\\/secure.gravatar.com\\\/avatar\\\/77997fb123ed6295d07f6612ad5a1afc8283a96f9c379981b21365a22e2cff35?s=96&d=mm&r=g\",\"caption\":\"Vo Giang\"},\"description\":\"M\u00ecnh l\u00e0 Giang, m\u1ed9t ng\u01b0\u1eddi k\u1ec3 chuy\u1ec7n c\u00f4ng ngh\u1ec7, ch\u1ecdn c\u00e1ch tr\u1ea3i nghi\u1ec7m v\u00e0 chia s\u1ebb nh\u1eefng gi\u1ea3i ph\u00e1p th\u1ef1c t\u1ebf. V\u1edbi m\u00ecnh, m\u1ed9t thi\u1ebft b\u1ecb t\u1ed1t ch\u1ec9 khi n\u00f3 th\u1ef1c s\u1ef1 l\u00e0m cho cu\u1ed9c s\u1ed1ng h\u00e0ng ng\u00e0y c\u1ee7a b\u1ea1n tr\u1edf n\u00ean d\u1ec5 d\u00e0ng v\u00e0 th\u00fa v\u1ecb h\u01a1n.\",\"sameAs\":[\"https:\\\/\\\/www.facebook.com\\\/hoanghamobilecom\"],\"url\":\"https:\\\/\\\/hoanghamobile.com\\\/tin-tuc\\\/author\\\/giang-vo\\\/\"}]}<\/script>\n<!-- \/ Yoast SEO Premium plugin. -->","yoast_head_json":{"title":"Nh\u1ecb th\u1ee9c Newton: c\u00f4ng th\u1ee9c v\u00e0 v\u00ed d\u1ee5","description":"Nh\u1ecb th\u1ee9c Newton l\u00e0 g\u00ec? C\u00f4ng th\u1ee9c khai tri\u1ec3n, s\u1ed1 h\u1ea1ng t\u1ed5ng qu\u00e1t, tam gi\u00e1c Pascal v\u00e0 b\u00e0i t\u1eadp c\u00f3 l\u1eddi gi\u1ea3i chi ti\u1ebft, d\u1ec5 hi\u1ec3u cho h\u1ecdc sinh l\u1edbp 10.","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/hoanghamobile.com\/tin-tuc\/nhi-thuc-newton\/","og_locale":"vi_VN","og_type":"article","og_title":"Nh\u1ecb th\u1ee9c Newton: c\u00f4ng th\u1ee9c khai tri\u1ec3n v\u00e0 v\u00ed d\u1ee5","og_description":"Nh\u1ecb th\u1ee9c Newton l\u00e0 g\u00ec? C\u00f4ng th\u1ee9c khai tri\u1ec3n, s\u1ed1 h\u1ea1ng t\u1ed5ng qu\u00e1t, tam gi\u00e1c Pascal v\u00e0 b\u00e0i t\u1eadp c\u00f3 l\u1eddi gi\u1ea3i chi ti\u1ebft, d\u1ec5 hi\u1ec3u cho h\u1ecdc sinh l\u1edbp 10.","og_url":"https:\/\/hoanghamobile.com\/tin-tuc\/nhi-thuc-newton\/","og_site_name":"Tin t\u1ee9c c\u00f4ng ngh\u1ec7 - HoangHaMobile","article_publisher":"https:\/\/www.facebook.com\/hoanghamobilecom","article_author":"https:\/\/www.facebook.com\/hoanghamobilecom","article_published_time":"2026-07-22T08:00:53+00:00","og_image":[{"width":1200,"height":628,"url":"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/nhi-thuc-newton.jpg","type":"image\/jpeg"}],"author":"Vo Giang","twitter_card":"summary_large_image","twitter_misc":{"\u0110\u01b0\u1ee3c vi\u1ebft b\u1edfi":"Vo Giang","\u01af\u1edbc t\u00ednh th\u1eddi gian \u0111\u1ecdc":"7 ph\u00fat"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/hoanghamobile.com\/tin-tuc\/nhi-thuc-newton\/#article","isPartOf":{"@id":"https:\/\/hoanghamobile.com\/tin-tuc\/nhi-thuc-newton\/"},"author":{"name":"Vo Giang","@id":"https:\/\/hoanghamobile.com\/tin-tuc\/#\/schema\/person\/72d0493d28396e6a0cdc358e9260c03c"},"headline":"Nh\u1ecb th\u1ee9c Newton: c\u00f4ng th\u1ee9c khai tri\u1ec3n v\u00e0 v\u00ed d\u1ee5","datePublished":"2026-07-22T08:00:53+00:00","mainEntityOfPage":{"@id":"https:\/\/hoanghamobile.com\/tin-tuc\/nhi-thuc-newton\/"},"wordCount":2095,"publisher":{"@id":"https:\/\/hoanghamobile.com\/tin-tuc\/#organization"},"image":{"@id":"https:\/\/hoanghamobile.com\/tin-tuc\/nhi-thuc-newton\/#primaryimage"},"thumbnailUrl":"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/nhi-thuc-newton.jpg","articleSection":["Th\u1ee7 thu\u1eadt"],"inLanguage":"vi","copyrightYear":"2026","copyrightHolder":{"@id":"https:\/\/hoanghamobile.com\/tin-tuc\/#organization"}},{"@type":"WebPage","@id":"https:\/\/hoanghamobile.com\/tin-tuc\/nhi-thuc-newton\/","url":"https:\/\/hoanghamobile.com\/tin-tuc\/nhi-thuc-newton\/","name":"Nh\u1ecb th\u1ee9c Newton: c\u00f4ng th\u1ee9c v\u00e0 v\u00ed d\u1ee5","isPartOf":{"@id":"https:\/\/hoanghamobile.com\/tin-tuc\/#website"},"primaryImageOfPage":{"@id":"https:\/\/hoanghamobile.com\/tin-tuc\/nhi-thuc-newton\/#primaryimage"},"image":{"@id":"https:\/\/hoanghamobile.com\/tin-tuc\/nhi-thuc-newton\/#primaryimage"},"thumbnailUrl":"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/nhi-thuc-newton.jpg","datePublished":"2026-07-22T08:00:53+00:00","description":"Nh\u1ecb th\u1ee9c Newton l\u00e0 g\u00ec? C\u00f4ng th\u1ee9c khai tri\u1ec3n, s\u1ed1 h\u1ea1ng t\u1ed5ng qu\u00e1t, tam gi\u00e1c Pascal v\u00e0 b\u00e0i t\u1eadp c\u00f3 l\u1eddi gi\u1ea3i chi ti\u1ebft, d\u1ec5 hi\u1ec3u cho h\u1ecdc sinh l\u1edbp 10.","breadcrumb":{"@id":"https:\/\/hoanghamobile.com\/tin-tuc\/nhi-thuc-newton\/#breadcrumb"},"inLanguage":"vi","potentialAction":[{"@type":"ReadAction","target":["https:\/\/hoanghamobile.com\/tin-tuc\/nhi-thuc-newton\/"]}]},{"@type":"ImageObject","inLanguage":"vi","@id":"https:\/\/hoanghamobile.com\/tin-tuc\/nhi-thuc-newton\/#primaryimage","url":"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/nhi-thuc-newton.jpg","contentUrl":"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/nhi-thuc-newton.jpg","width":1200,"height":628,"caption":"nhi-thuc-newton"},{"@type":"BreadcrumbList","@id":"https:\/\/hoanghamobile.com\/tin-tuc\/nhi-thuc-newton\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Trang ch\u1ee7","item":"https:\/\/hoanghamobile.com\/tin-tuc\/"},{"@type":"ListItem","position":2,"name":"Nh\u1ecb th\u1ee9c Newton: c\u00f4ng th\u1ee9c khai tri\u1ec3n v\u00e0 v\u00ed d\u1ee5"}]},{"@type":"WebSite","@id":"https:\/\/hoanghamobile.com\/tin-tuc\/#website","url":"https:\/\/hoanghamobile.com\/tin-tuc\/","name":"Tin t\u1ee9c c\u00f4ng ngh\u1ec7 - HoangHaMobile","description":"","publisher":{"@id":"https:\/\/hoanghamobile.com\/tin-tuc\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/hoanghamobile.com\/tin-tuc\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"vi"},{"@type":"Organization","@id":"https:\/\/hoanghamobile.com\/tin-tuc\/#organization","name":"Tin t\u1ee9c c\u00f4ng ngh\u1ec7 - HoangHaMobile","url":"https:\/\/hoanghamobile.com\/tin-tuc\/","logo":{"@type":"ImageObject","inLanguage":"vi","@id":"https:\/\/hoanghamobile.com\/tin-tuc\/#\/schema\/logo\/image\/","url":"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2021\/12\/logo-text.png","contentUrl":"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2021\/12\/logo-text.png","width":256,"height":37,"caption":"Tin t\u1ee9c c\u00f4ng ngh\u1ec7 - HoangHaMobile"},"image":{"@id":"https:\/\/hoanghamobile.com\/tin-tuc\/#\/schema\/logo\/image\/"},"sameAs":["https:\/\/www.facebook.com\/hoanghamobilecom"]},{"@type":"Person","@id":"https:\/\/hoanghamobile.com\/tin-tuc\/#\/schema\/person\/72d0493d28396e6a0cdc358e9260c03c","name":"Vo Giang","image":{"@type":"ImageObject","inLanguage":"vi","@id":"https:\/\/secure.gravatar.com\/avatar\/77997fb123ed6295d07f6612ad5a1afc8283a96f9c379981b21365a22e2cff35?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/77997fb123ed6295d07f6612ad5a1afc8283a96f9c379981b21365a22e2cff35?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/77997fb123ed6295d07f6612ad5a1afc8283a96f9c379981b21365a22e2cff35?s=96&d=mm&r=g","caption":"Vo Giang"},"description":"M\u00ecnh l\u00e0 Giang, m\u1ed9t ng\u01b0\u1eddi k\u1ec3 chuy\u1ec7n c\u00f4ng ngh\u1ec7, ch\u1ecdn c\u00e1ch tr\u1ea3i nghi\u1ec7m v\u00e0 chia s\u1ebb nh\u1eefng gi\u1ea3i ph\u00e1p th\u1ef1c t\u1ebf. V\u1edbi m\u00ecnh, m\u1ed9t thi\u1ebft b\u1ecb t\u1ed1t ch\u1ec9 khi n\u00f3 th\u1ef1c s\u1ef1 l\u00e0m cho cu\u1ed9c s\u1ed1ng h\u00e0ng ng\u00e0y c\u1ee7a b\u1ea1n tr\u1edf n\u00ean d\u1ec5 d\u00e0ng v\u00e0 th\u00fa v\u1ecb h\u01a1n.","sameAs":["https:\/\/www.facebook.com\/hoanghamobilecom"],"url":"https:\/\/hoanghamobile.com\/tin-tuc\/author\/giang-vo\/"}]}},"_links":{"self":[{"href":"https:\/\/hoanghamobile.com\/tin-tuc\/wp-json\/wp\/v2\/posts\/567199","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/hoanghamobile.com\/tin-tuc\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/hoanghamobile.com\/tin-tuc\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/hoanghamobile.com\/tin-tuc\/wp-json\/wp\/v2\/users\/65"}],"replies":[{"embeddable":true,"href":"https:\/\/hoanghamobile.com\/tin-tuc\/wp-json\/wp\/v2\/comments?post=567199"}],"version-history":[{"count":4,"href":"https:\/\/hoanghamobile.com\/tin-tuc\/wp-json\/wp\/v2\/posts\/567199\/revisions"}],"predecessor-version":[{"id":569063,"href":"https:\/\/hoanghamobile.com\/tin-tuc\/wp-json\/wp\/v2\/posts\/567199\/revisions\/569063"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/hoanghamobile.com\/tin-tuc\/wp-json\/wp\/v2\/media\/568950"}],"wp:attachment":[{"href":"https:\/\/hoanghamobile.com\/tin-tuc\/wp-json\/wp\/v2\/media?parent=567199"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/hoanghamobile.com\/tin-tuc\/wp-json\/wp\/v2\/categories?post=567199"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/hoanghamobile.com\/tin-tuc\/wp-json\/wp\/v2\/tags?post=567199"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}