{"id":63,"date":"2023-09-17T07:20:31","date_gmt":"2023-09-17T07:20:31","guid":{"rendered":"https:\/\/mathority.org\/cn\/%e4%ba%8c%e9%a1%b9%e5%bc%8f%e6%88%96%e7%89%9b%e9%a1%bf%e4%ba%8c%e9%a1%b9%e5%bc%8f%e5%ae%9a%e7%90%86%e5%85%ac%e5%bc%8f%e5%92%8c%e5%b7%b2%e8%a7%a3%e5%86%b3%e7%9a%84%e7%bb%83%e4%b9%a0\/"},"modified":"2023-09-17T07:20:31","modified_gmt":"2023-09-17T07:20:31","slug":"%e4%ba%8c%e9%a1%b9%e5%bc%8f%e6%88%96%e7%89%9b%e9%a1%bf%e4%ba%8c%e9%a1%b9%e5%bc%8f%e5%ae%9a%e7%90%86%e5%85%ac%e5%bc%8f%e5%92%8c%e5%b7%b2%e8%a7%a3%e5%86%b3%e7%9a%84%e7%bb%83%e4%b9%a0","status":"publish","type":"post","link":"https:\/\/mathority.org\/cn\/%e4%ba%8c%e9%a1%b9%e5%bc%8f%e6%88%96%e7%89%9b%e9%a1%bf%e4%ba%8c%e9%a1%b9%e5%bc%8f%e5%ae%9a%e7%90%86%e5%85%ac%e5%bc%8f%e5%92%8c%e5%b7%b2%e8%a7%a3%e5%86%b3%e7%9a%84%e7%bb%83%e4%b9%a0\/","title":{"rendered":"\u725b\u987f\u4e8c\u9879\u5f0f\uff08\u4e8c\u9879\u5f0f\u5b9a\u7406\uff09"},"content":{"rendered":"<p>\u5728\u6b64\u9875\u9762\u4e0a\uff0c\u60a8\u5c06\u627e\u5230\u725b\u987f\u4e8c\u9879\u5f0f\uff08\u6216\u4e8c\u9879\u5f0f\u5b9a\u7406\uff09\u53ca\u5176\u516c\u5f0f\u7684\u89e3\u91ca\u3002\u60a8\u8fd8\u53ef\u4ee5\u770b\u5230\u5982\u4f55\u4f7f\u7528\u5854\u5854\u5229\u4e9a\uff08\u6216\u5e15\u65af\u5361\uff09\u4e09\u89d2\u5f62\u6765\u7b80\u5316\u8fd9\u4e00\u8fc7\u7a0b\u3002\u6b64\u5916\uff0c\u60a8\u8fd8\u5c06\u627e\u5230\u725b\u987f\u4e8c\u9879\u5f0f\u53ca\u5176\u6240\u6709\u5c5e\u6027\u7684\u5206\u6b65\u89e3\u7b54\u7ec3\u4e60\u3002\u6700\u540e\uff0c\u6211\u4eec\u5c06\u89e3\u91ca\u8fd9\u4e2a\u975e\u5e38\u7279\u6b8a\u7684\u5b9a\u7406\u8d77\u6e90\u80cc\u540e\u7684\u597d\u5947\u5fc3\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%C2%BFQue-es-el-binomio-de-Newton\"><\/span>\u4ec0\u4e48\u662f\u725b\u987f\u4e8c\u9879\u5f0f\uff1f <span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p class=\"has-background\" style=\"background-color:#ffebee\">\u5728\u6570\u5b66\u4e2d\uff0c<strong>\u725b\u987f\u4e8c\u9879\u5f0f<\/strong>\uff0c\u4e5f\u79f0\u4e3a<strong>\u4e8c\u9879\u5f0f\u5b9a\u7406<\/strong>\uff0c\u662f\u4e00\u4e2a\u53ef\u4ee5\u8ba9\u60a8\u8f7b\u677e\u8ba1\u7b97\u4e8c\u9879\u5f0f\u5e42\u7684\u516c\u5f0f\u3002\u6362\u53e5\u8bdd\u8bf4\uff0c\u725b\u987f\u4e8c\u9879\u5f0f\u7531\u4e00\u4e2a\u53ef\u4ee5<sup>\u6c42\u89e3<\/sup>(a+b) \u5f62\u5f0f\u7684\u4ee3\u6570\u8868\u8fbe\u5f0f\u7684\u516c\u5f0f\u7ec4\u6210\u3002<\/p>\n<p>\u663e\u7136\uff0c\u8fd9\u4e2a\u5b9a\u7406\u662f\u4ee5\u7269\u7406\u5b66\u5bb6\u3001\u6570\u5b66\u5bb6\u548c\u54f2\u5b66\u5bb6\u827e\u8428\u514b\u00b7\u725b\u987f\u7235\u58eb\u7684\u540d\u5b57\u547d\u540d\u7684\u3002\u7136\u800c\uff0c\u5728\u8fd9\u65b9\u9762\u5b58\u5728\u4e00\u4e9b\u4e89\u8bae\uff0c\u56e0\u4e3a\u5728\u4e2d\u4e1c\u6587\u672c\u4e2d\u5df2\u7ecf\u53d1\u73b0\u4e86\u8be5\u5b9a\u7406\u7684\u4f7f\u7528\u3002\u4e0b\u9762\u6211\u4eec\u5c31\u6df1\u5165\u63a2\u8ba8\u4e00\u4e0b\u8fd9\u4e2a\u6570\u5b66\u516c\u5f0f\u7684\u7531\u6765\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Formula-del-binomio-de-Newton\"><\/span>\u725b\u987f\u4e8c\u9879\u5f0f\u516c\u5f0f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u6b63\u5982\u6211\u4eec\u5728\u725b\u987f\u4e8c\u9879\u5f0f\u7684\u5b9a\u4e49\u4e2d\u770b\u5230\u7684\uff0c\u8be5\u5b9a\u7406\u7528\u4e8e\u6c42\u89e3\u4e8c\u9879\u5f0f\u7684\u5e42\u3002\u4f46\u662f\u2026\u2026\u725b\u987f\u4e8c\u9879\u5f0f\u662f\u5982\u4f55\u5e94\u7528\u7684\uff1f\u6216\u8005\uff0c\u6362\u53e5\u8bdd\u8bf4\uff0c\u725b\u987f\u4e8c\u9879\u5f0f\u516c\u5f0f\u662f\u4ec0\u4e48\uff1f <\/p>\n<div style=\"background-color:#ffebee;padding-top: 20px; padding-bottom: 0.5px; padding-right: 40px; padding-left: 30px; border-radius:20px;\">\n<p style=\"text-align:left\"><strong>\u725b\u987f\u4e8c\u9879\u5f0f\u7684\u6570\u5b66\u516c\u5f0f<\/strong>\u5982\u4e0b\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8087bb711e716aca4a2c535eaeb8b0bf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\left( a+b\\right)^n = &amp; \\sum_{k=0}^{n}\\begin{pmatrix} n\\\\ k\\end{pmatrix}a^{n-k}b^k\" title=\"Rendered by QuickLaTeX.com\" height=\"50\" width=\"204\" style=\"vertical-align: -22px;\"><\/p>\n<\/p>\n<p>\u6216\u540c\u7b49\u5b66\u5386\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-19bab1dcab88a71b5b3bed39bf09cc73_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left( a+b\\right)^n =\\begin{pmatrix} n \\\\ 0 \\end{pmatrix} \\right)a^n b^0 + \\begin{pmatrix} n \\\\ 1 \\end{pmatrix} a^{n-1}b^{1} + \\begin{pmatrix} n \\\\ 2 \\end{pmatrix} a^{n-2}b^{2} + \\dots + \\begin{pmatrix} n \\\\ n \\end{pmatrix} a^0 b^{n}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"520\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<\/div>\n<p>\u8be5\u516c\u5f0f\u5bf9\u4e8e\u7406\u89e3\u725b\u987f\u4e8c\u9879\u5f0f\u7684\u6982\u5ff5\u6765\u8bf4\u6709\u70b9\u590d\u6742\uff0c\u56e0\u6b64\u6211\u4eec\u5728\u4e0b\u9762\u5217\u51fa\u4e86\u6700\u4f4e\u6b21\u4e8c\u9879\u5f0f\u7684\u5e42\uff0c\u4ee5\u4fbf\u60a8\u66f4\u597d\u5730\u7406\u89e3\u5b83\uff1a <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/formule-binomiale-ou-theoreme-de-newton.jpg\" alt=\"\u725b\u987f\u4e8c\u9879\u5f0f\u5b9a\u7406\u7684\u516c\u5f0f\" class=\"wp-image-2126\" width=\"578\" height=\"578\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p>\u6b63\u5982\u60a8\u6240\u770b\u5230\u7684\uff0c\u5c55\u5f00\u4e8c\u9879\u5f0f \u65f6<strong>\uff0c\u7b2c\u4e00\u9879 (a) \u7684\u6307\u6570\u51cf\u5c11<\/strong>\uff0c\u800c<strong>\u7b2c\u4e8c\u9879 (b) \u7684\u6307\u6570\u589e\u52a0<\/strong>\uff0c\u5c31\u50cf\u7ec4\u5408\u6570\u7684\u8f83\u4f4e\u5143\u7d20\u589e\u52a0\u4e00\u6837\u3002<\/p>\n<p>\u56e0\u6b64\uff0c\u8981\u4f7f\u7528\u4e8c\u9879\u5f0f\u5b9a\u7406\uff0c\u60a8\u9700\u8981\u77e5\u9053\u5982\u4f55\u6c42\u89e3\u7ec4\u5408\u6570\uff0c\u5373\u7c7b\u578b\u7684\u4ee3\u6570\u8868\u8fbe\u5f0f<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-59b5fcabfa89714b1a55cbd237e405ab_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{pmatrix} 4 \\\\ 2 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"29\" style=\"vertical-align: -17px;\"><\/p>\n<p>\u3002\u56e0\u6b64\uff0c\u5728\u6211\u4eec\u67e5\u770b\u5982\u4f55\u8ba1\u7b97\u725b\u987f\u4e8c\u9879\u5f0f\u7684\u793a\u4f8b\u4e4b\u524d\uff0c\u8ba9\u6211\u4eec\u7b80\u8981\u56de\u987e\u4e00\u4e0b\u7ec4\u5408\u6570\u3002<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Numero-combinatorio\"><\/span>\u7ec4\u5408\u6570<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u8981\u786e\u5b9a<strong>\u7ec4\u5408\u6570<\/strong>\uff08\u6216\u4e8c\u9879\u5f0f\u7cfb\u6570\uff09\uff0c\u60a8\u5fc5\u987b\u5e94\u7528\u4ee5\u4e0b\u516c\u5f0f\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b0b6e9d4f65b3670d26dabb0141b15fa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{pmatrix}n \\\\ k \\end{pmatrix} = \\cfrac{n!}{k!(n-k)!}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"135\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u91d1\u5b50<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-da0ef996f36e1b32a0f26f6e896e1771_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n!\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"15\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u548c<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ef344500b3e227ba2eebac8f79f8229a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"k!\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"14\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u8fd9\u4e9b\u662f<strong>\u9636\u4e58\u6570<\/strong>\u3002\u6211\u4eec\u8fd8\u8bf7\u8bb0\u4f4f\uff0c\u9636\u4e58\u6570\u662f\u901a\u8fc7\u5c06\u6240\u6709 1 \u7684\u6b63\u6574\u6570\u4e58\u4ee5\u6240\u8ff0\u6570\u6765\u8ba1\u7b97\u7684\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-09df3296b34c0da43f17d367af376ce5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n! = 1 \\cdot 2 \\cdot 3 \\cdots (n-1) \\cdot n\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"197\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u4f5c\u4e3a\u793a\u4f8b\uff0c\u6211\u4eec\u5c06\u627e\u5230\u4e00\u4e2a\u7ec4\u5408\u6570\uff0c\u4ee5\u4fbf\u60a8\u4e86\u89e3\u5b83\u662f\u5982\u4f55\u5b8c\u6210\u7684\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-619109bf5a34808b1f72ef6799a75482_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{pmatrix} 4\\\\ 3 \\end{pmatrix} = \\cfrac{4!}{3!(4-3)!}=\\cfrac{4!}{3!\\cdot 1!}= \\cfrac{1 \\cdot 2\\cdot 3 \\cdot 4}{(1 \\cdot 2\\cdot 3) \\cdot 1} = \\cfrac{24}{6} = 4\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"385\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u7ec4\u5408\u6570\u4e5f\u53ef\u4ee5\u901a\u8fc7\u8ba1\u7b97\u5668\u7528 \u952e\u786e\u5b9a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-840c7e15e97f9fa0c5615b063966e20e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\boxed{nCr}.\" title=\"Rendered by QuickLaTeX.com\" height=\"24\" width=\"48\" style=\"vertical-align: -6px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Ejemplos-del-binomio-de-Newton\"><\/span>\u725b\u987f\u4e8c\u9879\u5f0f\u793a\u4f8b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u73b0\u5728\u6211\u4eec\u77e5\u9053\u4ec0\u4e48\u662f\u4e8c\u9879\u5f0f\u5b9a\u7406\uff0c\u8ba9\u6211\u4eec\u770b\u770b\u5982\u4f55\u4f7f\u7528\u4e24\u4e2a\u6570\u503c\u793a\u4f8b\u6765\u5e94\u7528\u725b\u987f\u4e8c\u9879\u5f0f\u516c\u5f0f\u3002<\/p>\n<h3 class=\"wp-block-heading\">\u5b9e\u65bd\u4f8b1<\/h3>\n<ul>\n<li>\u5e94\u7528\u725b\u987f\u4e8c\u9879\u5f0f\u8ba1\u7b97\u4ee5\u4e0b\u4e8c\u9879\u5f0f\u7684\u5e42\uff1a<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-765733b5fff1862758f20d820c234683_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x+3)^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"61\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u663e\u7136\uff0c\u7531\u4e8e\u8fd9\u4e2a\u4e8c\u9879\u5f0f\u662f\u5e73\u65b9\u7684\uff0c\u6240\u4ee5\u4e5f\u53ef\u4ee5\u7528\u663e\u7740\u6052\u7b49\u5f0f\u7684\u516c\u5f0f\u6765\u6c42\u89e3\uff08 <strong><span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/cn\/\u6052\u7b49\u5f0f\u4ea7\u54c1-\u663e\u7740\u7684\u7b49\u5f0f\u89e3\u51b3\u7ec3\u4e60\/\">\u5982\u4f55\u6c42\u89e3\u663e\u7740\u6052\u7b49\u5f0f<\/a><\/span><\/strong>\uff09\uff0c\u4f46\u6211\u4eec\u5c06\u4ee5\u4e8c\u9879\u5f0f\u5b9a\u7406\u4e3a\u4f8b\u8fdb\u884c\u8ba1\u7b97\u3002<\/p>\n<p>\u9996\u5148\uff0c\u6211\u4eec\u5fc5\u987b\u5e94\u7528\u725b\u987f\u4e8c\u9879\u5f0f\u516c\u5f0f\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-19bab1dcab88a71b5b3bed39bf09cc73_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left( a+b\\right)^n =\\begin{pmatrix} n \\\\ 0 \\end{pmatrix} \\right)a^n b^0 + \\begin{pmatrix} n \\\\ 1 \\end{pmatrix} a^{n-1}b^{1} + \\begin{pmatrix} n \\\\ 2 \\end{pmatrix} a^{n-2}b^{2} + \\dots + \\begin{pmatrix} n \\\\ n \\end{pmatrix} a^0 b^{n}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"520\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b n=2\uff0c\u56e0\u6b64\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e75e12f24582b099635b2287594fbd00_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left( x+3\\right)^2 =\\begin{pmatrix} 2 \\\\ 0 \\end{pmatrix} \\right)x^2 \\cdot 3^0 + \\begin{pmatrix} 2 \\\\ 1 \\end{pmatrix} x^1\\cdot3^1 + \\begin{pmatrix} 2 \\\\ 2 \\end{pmatrix} x^{0}\\cdot3^{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"383\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u4ed4\u7ec6\u770b\uff0c\u4e00\u5f00\u59cb\u6211\u4eec\u5c06\u7b2c\u4e00\u9879 (x) \u63d0\u9ad8\u5230\u53ef\u80fd\u7684\u6700\u5927\u503c\uff0c\u5728\u672c\u4f8b\u4e2d\u4e3a 2\u3002\u53e6\u4e00\u65b9\u9762\uff0c\u6211\u4eec\u5c06\u7b2c\u4e8c\u9879 (3) \u63d0\u9ad8\u5230\u53ef\u80fd\u7684\u6700\u5c0f\u503c\uff0c\u5b83\u59cb\u7ec8\u4e3a 0\u3002\u4f46\u662f\u5f53\u6211\u4eec\u5411\u53f3\u79fb\u52a8\u65f6\uff0c\u6211\u4eec\u9700\u8981\u5c06<strong>\u7b2c\u4e00\u9879\u63d0\u9ad8\u5230\u6bd4\u4ee5\u524d\u66f4\u4f4e\u7684\u6570\u5b57<\/strong>\uff0c\u5c06<strong>\u7b2c\u4e8c\u9879\u63d0\u9ad8\u5230\u6bd4\u4ee5\u524d\u66f4\u9ad8\u7684\u6570\u5b57\u3002<\/strong><\/p>\n<p>\u73b0\u5728\u6211\u4eec\u6765\u8ba1\u7b97\u7ec4\u5408\u6570\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-541c34c91eb3c95f11be4b0e19a9a882_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left( x+3\\right)^2 =1\\cdot x^2\\cdot 3^0 + 2\\cdot x^1\\cdot 3^1 + 1\\cdot x^{0}\\cdot 3^{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"334\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u6211\u4eec\u6c42\u89e3\u6743\u529b\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ba9ed22a3248d243b7298f36be657c7e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left( x+3\\right)^2 =1\\cdot x^2\\cdot 1 + 2\\cdot x\\cdot 3 + 1\\cdot 1\\cdot 9\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"295\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u6700\u540e\uff0c\u6211\u4eec\u8ba1\u7b97\u4e58\u6cd5\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d43c304356e20edd6c9b63e0703a279f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left( x+3\\right)^2 =x^2 + 6x + 9\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"174\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\">\u5b9e\u65bd\u4f8b2<\/h3>\n<p>\u73b0\u5728\u6211\u4eec\u8981\u89e3\u51b3\u4e00\u4e2a\u7a0d\u5fae\u56f0\u96be\u4e00\u70b9\u7684\u95ee\u9898\u3002<\/p>\n<ul>\n<li>\u5e94\u7528\u725b\u987f\u4e8c\u9879\u5f0f\u516c\u5f0f\u6c42\u4ee5\u4e0b\u4e8c\u9879\u5f0f\u7684\u5e42\uff1a<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5466a47ebcb4446937988adabd0c64f3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(2x+1)^3\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"70\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u4e8c\u9879\u5f0f\u5b9a\u7406\u7684\u516c\u5f0f\u4e3a\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-19bab1dcab88a71b5b3bed39bf09cc73_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left( a+b\\right)^n =\\begin{pmatrix} n \\\\ 0 \\end{pmatrix} \\right)a^n b^0 + \\begin{pmatrix} n \\\\ 1 \\end{pmatrix} a^{n-1}b^{1} + \\begin{pmatrix} n \\\\ 2 \\end{pmatrix} a^{n-2}b^{2} + \\dots + \\begin{pmatrix} n \\\\ n \\end{pmatrix} a^0 b^{n}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"520\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0cn=3\uff0c\u56e0\u6b64\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e55cd40782bdb46907860c3e04c49fbe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left( 2x+1\\right)^3 =\\begin{pmatrix} 3 \\\\ 0 \\end{pmatrix} \\right)(2x)^3 \\cdot 1^0 + \\begin{pmatrix} 3 \\\\ 1 \\end{pmatrix} (2x)^{2}\\cdot 1^1 + \\begin{pmatrix} 3 \\\\ 2 \\end{pmatrix} (2x)^{1}\\cdot 1^{2} + \\begin{pmatrix} 3 \\\\ 3 \\end{pmatrix} (2x)^{0}\\cdot 1^{3}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"589\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u6211\u4eec\u8ba1\u7b97\u7ec4\u5408\u6570\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d7ff5e4d9ee6990d854f22059f7db0d9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left( 2x+1\\right)^3 =1\\cdot (2x)^3 \\cdot 1^0 + 3\\cdot (2x)^{2}\\cdot 1^1 + 3 \\cdot (2x)^{1}\\cdot 1^{2} + 1\\cdot (2x)^{0}\\cdot 1^{3}\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"524\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u73b0\u5728\u6211\u4eec\u89e3\u51b3\u6743\u529b\u95ee\u9898\uff0c\u4e3a\u6b64\uff0c\u8bb0\u4f4f\u4ee5\u4e0b\u4e24\u4e2a\u5c5e\u6027\u5f88\u91cd\u8981\uff1a<\/p>\n<p class=\"has-background\" style=\"background-color:#fffde7\"> \u2022 \u5f53\u5355\u9879\u5f0f\u5347\u4e3a\u6307\u6570\u65f6\uff0c\u7cfb\u6570\u548c\u53d8\u91cf\u5347\u4e3a\u76f8\u540c\u7684\u6307\u6570 \u2192<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3426c618ed82b8baf60f97603a2e17f9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(2x)^3=2^3\\cdot x^3 =8\\cdot x^3 =8x^3\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"223\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u2022 \u4efb\u4f55\u9879\u53d8\u4e3a 0 \u90fd\u4f1a\u5f97\u5230 1 \u2192<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-cdfedc209dec05e7c24c7b35478e795b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(2x)^0=1\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"71\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c\u6211\u4eec\u901a\u8fc7\u8fd9\u4e24\u4e2a\u5c5e\u6027\u627e\u5230\u6743\u529b\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-97b81539ae095cd73e1054b74e5fe5c4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left( 2x+1\\right)^3 =1\\cdot 2^3x^3 \\cdot 1 + 3\\cdot 2^2x^{2}\\cdot 1 + 3 \\cdot 2^1x^{1}\\cdot 1 + 1\\cdot 1\\cdot 1\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"443\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-825eca438cd77124fb64e987aef09e39_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left( 2x+1\\right)^3 =1\\cdot 8x^3 \\cdot 1 + 3\\cdot 4x^{2}\\cdot 1 + 3 \\cdot 2x\\cdot 1 + 1\\cdot 1\\cdot 1\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"412\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u6700\u540e\uff0c\u6211\u4eec\u5c06\u8fd9\u4e9b\u9879\u76f8\u4e58\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d666ed4bb3a25b85121e7b8be0e7295e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left( 2x+1\\right)^3 =8x^3 + 12x^{2}+6x + 1\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"248\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"El-binomio-de-Newton-y-el-triangulo-de-Tartaglia-o-de-Pascal\"><\/span>\u725b\u987f\u4e8c\u9879\u5f0f\u548c\u5854\u5854\u5229\u4e9a\uff08\u6216\u5e15\u65af\u5361\uff09\u4e09\u89d2\u5f62<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u6b63\u5982\u60a8\u5728\u4e0a\u9762\u7684\u793a\u4f8b\u4e2d\u770b\u5230\u7684\uff0c\u8ba1\u7b97\u7ec4\u5408\u6570\u6709\u70b9\u4e4f\u5473\u3002\u8fd9\u5c31\u662f\u4e3a\u4ec0\u4e48\u6211\u4eec\u8981\u6559\u4f60\u4e00\u4e2a\u6280\u5de7\uff0c\u8fd9\u6837\u4f60\u5c31\u4e0d\u5fc5\u89e3\u7ec4\u5408\u6570\uff0c\u56e0\u4e3a\u4f60\u53ef\u4ee5\u4f7f\u7528\u5854\u5854\u5229\u4e9a\u4e09\u89d2\u5f62\uff08\u4e5f\u79f0\u4e3a\u5e15\u65af\u5361\u4e09\u89d2\u5f62\uff09\u76f4\u63a5\u627e\u51fa\u5b83\u4eec\u7684\u4ef7\u503c\u3002<\/p>\n<p>\u5982\u679c\u60a8\u4e0d\u77e5\u9053\u5b83\u662f\u4ec0\u4e48\uff0c<strong>\u5854\u5854\u5229\u4e9a\u4e09\u89d2\u5f62<\/strong>\uff0c\u4e5f\u79f0\u4e3a<strong>\u5e15\u65af\u5361\u4e09\u89d2\u5f62<\/strong>\uff0c\u662f\u6392\u5217\u6210\u4e09\u89d2\u5f62\u7684\u6570\u5b57\u7684\u6570\u5b66\u8868\u793a\u3002<\/p>\n<p>\u8981\u6784\u5efa\u5854\u5854\u5229\u4e9a\u6216\u5e15\u65af\u5361\u4e09\u89d2\u5f62\uff0c\u6211\u4eec\u5fc5\u987b\u4ece\u4e09\u89d2\u5f62\u7684\u9876\u70b9\u5f00\u59cb\uff0c\u8be5\u9876\u70b9\u59cb\u7ec8\u4e3a 1\uff0c\u7136\u540e\u786e\u5b9a\u4e0b\u9762\u7684\u7ebf\u7684\u6570\u91cf\u3002\u4ee5\u4e0b\u5404\u884c\u4e2d\u7684\u6bcf\u4e2a\u6570\u5b57\u90fd\u7b49\u4e8e\u7d27\u90bb\u5176\u4e0a\u65b9\u7684\u4e24\u4e2a\u6570\u5b57\u4e4b\u548c\uff0c\u4f46\u884c\u5c3e\u59cb\u7ec8\u4e3a 1 \u9664\u5916\u3002 <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/comment-construire-le-triangle-tartaglia-de-pascal.jpg\" alt=\"\u725b\u987f\u914d\u5bf9 1 \u9ad8\u4e2d\u5728\u7ebf\" class=\"wp-image-1936\" width=\"220\" height=\"288\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p>\u90a3\u4e48\uff0c\u5854\u5854\u5229\u4e9a\u4e09\u89d2\u5f62\u4e2d\u7684\u6bcf\u4e00\u4e2a\u6570\u5b57\u90fd\u5bf9\u5e94\u7740\u4e00\u4e2a\u7ec4\u5408\u6570\u7684\u7ed3\u679c\uff0c\u770b\u4e0b\u56fe\uff1a <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/tirangulo-de-tartaglia-pascal-nombres-combinatoires.jpg\" alt=\"\" class=\"wp-image-1969\" width=\"538\" height=\"204\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p>\u4f8b\u5982\uff0c\u4e8c\u9879\u5f0f\u7cfb\u6570<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b9c97b98e22e9867a562555c1a3db2d8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{pmatrix} 3 \\\\ 1 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"29\" style=\"vertical-align: -17px;\"><\/p>\n<p>\u7b49\u4e8e3\uff0c\u56e0\u4e3a\u5728\u5854\u5c14\u5854\u5229\u4e9a\u4e09\u89d2\u5f62\u4e2d\uff0c\u5b83\u7684\u4f4d\u7f6e\u6709\u4e00\u4e2a3\u3002<\/p>\n<p>\u56e0\u6b64\uff0c\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u5854\u5854\u5229\u4e9a\uff08\u6216\u5e15\u65af\u5361\uff09\u4e09\u89d2\u5f62\u66f4\u5feb\u5730\u6c42\u89e3\u725b\u987f\u4e8c\u9879\u5f0f\uff0c\u56e0\u4e3a\u5b83\u4f7f\u6211\u4eec\u65e0\u9700\u8ba1\u7b97\u7ec4\u5408\u6570\u3002<\/p>\n<p>\u4f8b\u5982\uff0c\u5982\u679c\u6211\u4eec\u60f3\u8981\u5bf9\u4e8c\u9879\u5f0f\u8fdb\u884c\u4ee5\u4e0b\u589e\u5f3a\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ebc694e191c443617943252538d68669_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x+5)^3\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"61\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u901a\u8fc7\u5e94\u7528\u725b\u987f\u4e8c\u9879\u5f0f\u6cd5\u5219\uff0c\u6211\u4eec\u5f97\u5230\u4ee5\u4e0b\u4ee3\u6570\u8868\u8fbe\u5f0f\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c519ee24ca58f3139893d7350189527f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left(x+5\\right)^3 =\\begin{pmatrix} 3 \\\\ 0 \\end{pmatrix} \\right)x^3 \\cdot 5^0 + \\begin{pmatrix} 3 \\\\ 1 \\end{pmatrix} x^{2}\\cdot 5^1 + \\begin{pmatrix} 3 \\\\ 2 \\end{pmatrix} x^{1}\\cdot 5^{2} + \\begin{pmatrix} 3 \\\\ 3 \\end{pmatrix} x^{0}\\cdot 5^{3}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"490\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u90a3\u4e48\uff0c\u6211\u4eec\u4e0d\u7528\u4e00\u4e00\u8ba1\u7b97\u7ec4\u5408\u6570\uff0c\u800c\u662f\u7b80\u5355\u5730\u5c06\u6bcf\u4e2a\u7ec4\u5408\u6570\u66ff\u6362\u4e3a\u5854\u5854\u5229\u4e9a\u4e09\u89d2\u5f62\u5bf9\u5e94\u7684\u7cfb\u6570\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u4e8c\u9879\u5f0f\u88ab\u63d0\u5347\u5230\u7b2c\u4e09\u5c42\uff0c\u56e0\u6b64\u5b83\u5bf9\u5e94\u4e8e\u4e09\u89d2\u5f62\u7684\u7b2c\u4e09\u5c42\uff1a <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/triangle-de-tartaglia-et-binome-de-newton-ou-pascal.png\" alt=\"\u5854\u5c14\u5854\u5229\u4e9a\u6216\u5e15\u65af\u5361\u4e09\u89d2\u5f62\u548c\u725b\u987f\u4e8c\u9879\u5f0f\" class=\"wp-image-2041\" width=\"319\" height=\"218\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-137ba158b5fc348259d802391c34dfad_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left(x+5\\right)^3 =\\color{red} \\bm{1} \\color{black} \\cdot x^3 \\cdot 5^0 + \\color{red} \\bm{3} \\color{black}  \\cdot x^{2}\\cdot 5^1 + \\color{red} \\bm{3} \\color{black} \\cdot x^{1}\\cdot 5^{2} +\\color{red} \\bm{1} \\color{black} \\cdot x^{0}\\cdot 5^{3}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"582\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u73b0\u5728\u6211\u4eec\u8981\u505a\u7684\u5c31\u662f\u5b8c\u6210\u5269\u4e0b\u7684\u64cd\u4f5c\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-baa8da36add688734cd5c35e495e6326_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left(x+5\\right)^3 =1 \\cdot x^3 \\cdot 1 + 3\\cdot  x^{2}\\cdot 5 + 3 \\cdot x\\cdot 25 +1\\cdot 1\\cdot 125\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"404\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-fc2cf49b9bd743a6f47bde4ca0646b39_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left(x+5\\right)^3 =x^3+ 15x^2 + 75x +125\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"257\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u6b63\u5982\u60a8\u6240\u770b\u5230\u7684\uff0c\u5854\u5854\u5229\u4e9a\uff08\u6216\u5e15\u65af\u5361\uff09\u4e09\u89d2\u5f62\u7528\u4e8e\u4ee5\u66f4\u7b80\u5355\u3001\u66f4\u5feb\u7684\u65b9\u5f0f\u8ba1\u7b97\u725b\u987f\u4e8c\u9879\u5f0f\uff0c\u6b63\u5982\u6211\u4eec\u6240\u5c55\u793a\u7684\u3002\u8fd9\u5c31\u662f\u6211\u4eec\u5efa\u8bae\u4f7f\u7528\u5b83\u7684\u539f\u56e0\u3002<\/p>\n<p class=\"has-text-align-left\">\u603b\u7ed3\u5230\u76ee\u524d\u4e3a\u6b62\u6211\u4eec\u6240\u770b\u5230\u7684\u4e00\u5207\uff0c\u6211\u4eec\u7ed9\u60a8\u7559\u4e0b\u4e00\u5f20\u56fe\u50cf\uff0c\u663e\u793a\u725b\u987f\u4e8c\u9879\u5f0f\u4e0e\u5854\u5854\u5229\u4e9a\uff08\u6216\u5e15\u65af\u5361\uff09\u4e09\u89d2\u5f62\u7684\u6570\u5b57\u7684\u8868\u8fbe\u5f0f\u662f\u4ec0\u4e48\u6837\u7684\uff1a <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/binome-de-newton-et-triangle-de-pascal-ou-de-tartaglia-2.jpg\" alt=\"\u725b\u987f\u4e8c\u9879\u5f0f\u548c\u5e15\u65af\u5361\u4e09\u89d2\u5f62\u6216\u5854\u5854\u5229\u4e9a\" class=\"wp-image-2151\" width=\"535\" height=\"379\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Binomio-de-Newton-negativo-potencia-de-una-resta\"><\/span>\u8d1f\u725b\u987f\u4e8c\u9879\u5f0f\uff1a\u51cf\u6cd5\u5e42<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u5230\u76ee\u524d\u4e3a\u6b62\uff0c\u6211\u4eec\u89e3\u51b3\u7684\u6240\u6709\u725b\u987f\u4e8c\u9879\u5f0f\u7684\u4f8b\u5b50\u90fd\u662f\u52a0\u6cd5\u3002\u53e6\u4e00\u65b9\u9762\uff0c\u5f53\u4e8c\u9879\u5f0f\u7684\u4e24\u9879\u4e2d\u7684\u4e00\u9879\u5177\u6709\u8d1f\u53f7\u65f6\uff0c\u8fc7\u7a0b\u4fdd\u6301\u76f8\u4f3c\uff0c\u4f46\u7565\u6709\u53d8\u5316\u3002<\/p>\n<p class=\"has-background\" style=\"background-color:#ffebee\">\u5f53\u4e8c\u9879\u5f0f\u7684\u4e00\u9879\u4e3a\u8d1f\u65f6\uff0c\u4e5f\u5c31\u662f\u8bf4\u5b83\u662f (ab) <sup>n<\/sup>\u7c7b\u578b\u7684\u51cf\u6cd5\uff0c\u725b\u987f\u4e8c\u9879\u5f0f\u7684\u5c55\u5f00\u5f0f\u7684\u7b26\u53f7\u5fc5\u987b\u4ee5 + \u2013 + \u2013 + \u2013 + \u2013 \u2026 \u7684\u5f62\u5f0f\u4ea4\u66ff\u3002<\/p>\n<p>\u4e0b\u9762\u6211\u4eec\u7528\u4e8c\u9879\u5f0f\u5b9a\u7406\u548c\u5df2\u7ecf\u5b58\u5728\u7684\u5854\u5c14\u5854\u5229\u4e9a\u4e09\u89d2\u5f62\u7684\u7cfb\u6570\u5bfc\u51fa\u4e86\u524d5\u6b21\u8d1f\u4e8c\u9879\u5f0f\u7684\u5e42\uff0c\u8fd9\u6837\u60a8\u5c31\u53ef\u4ee5\u76f4\u63a5\u627e\u5230\u60a8\u9700\u8981\u7684\u4e8c\u9879\u5f0f\u8868\u8fbe\u5f0f\uff1a <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/puissance-binomiale-newton-negative-dune-soustraction-2.jpg\" alt=\"\u51cf\u6cd5 2 \u7684\u8d1f\u725b\u987f\u4e8c\u9879\u5f0f\u5e42\" class=\"wp-image-2147\" width=\"525\" height=\"387\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Propiedades-del-binomio-de-Newton\"><\/span>\u725b\u987f\u4e8c\u9879\u5f0f\u7684\u6027\u8d28<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u725b\u987f\u4e8c\u9879\u5f0f\u8868\u8fbe\u5f0f\u5177\u6709\u4ee5\u4e0b\u7279\u70b9\uff1a<\/p>\n<ul>\n<li>\u5206\u89e3\u725b\u987f\u4e8c\u9879\u5f0f\u603b\u662f\u4f1a\u5f97\u5230\u6bd4\u4e8c\u9879\u5f0f\u6b21\u6570\u591a\u7684\u4e00\u9879\u3002\u6216\u8005\u6362\u53e5\u8bdd\u8bf4\uff0c\u5bf9\u4e8e\u8fd9\u5bf9\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a7cb070eb92ff2ce3199cbbf72ab6122_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a+b)^n\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"60\" style=\"vertical-align: -5px;\"><\/p>\n<p>\u4ed6\u4eec\u53d7\u5230\u5f71\u54cd<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d72f4e3699652cfc70b8880515893d7c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n+1\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"40\" style=\"vertical-align: -2px;\"><\/p>\n<p>\u6761\u6b3e\u3002<\/li>\n<li>\u5143\u7d20\u7684\u529b\u91cf\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u4ece&#8230;\u5f00\u59cb<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b170995d512c659d8668b4e42e1fef6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u5e76\u4e14\u5728\u6700\u540e\u4e00\u4e2a\u5b63\u5ea6\u4e0b\u964d\u81f3 0\u3002<\/li>\n<li>\u5143\u7d20\u7684\u529b\u91cf\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"b\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u5b83\u4eec\u671d\u53e6\u4e00\u4e2a\u65b9\u5411\u53d1\u5c55\uff1a\u5b83\u4eec\u4ece 0 \u5f00\u59cb\u5e76\u589e\u52a0\uff0c\u76f4\u5230\u8fbe\u5230<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b170995d512c659d8668b4e42e1fef6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u5728\u6700\u540e\u4e00\u4e2a\u5b66\u671f\u3002<\/li>\n<li>\u5bf9\u4e8e\u725b\u987f\u4e8c\u9879\u5f0f\u7684\u6bcf\u4e2a\u5143\u7d20\uff0c\u6307\u6570\u4e4b\u548c\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u548c<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"b\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u7b49\u4e8e<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7ecab3f5df4767e23a2660ceb88ceabd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n.\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"15\" style=\"vertical-align: 0px;\"><\/p>\n<\/li>\n<li>\u725b\u987f\u4e8c\u9879\u5f0f\u8868\u8fbe\u5f0f\u7b2c\u4e00\u9879\u7684\u7cfb\u6570\u59cb\u7ec8\u4e3a 1\uff08\u6b63\uff09\uff0c\u7b2c\u4e8c\u4e2a\u7cfb\u6570\u76f8\u5f53\u4e8e\u4e8c\u9879\u5f0f\u7684\u6307\u6570\uff08\u6b63\u6216\u8d1f\uff09\u3002 <\/li>\n<\/ul>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Calcular-el-termino-k-esimo-del-binomio-de-Newton\"><\/span>\u8ba1\u7b97\u725b\u987f\u4e8c\u9879\u5f0f\u7684\u7b2c k \u9879<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u867d\u7136\u8fd9\u5f88\u4e0d\u5bfb\u5e38\uff0c\u4f46\u6211\u4eec\u6709\u65f6\u4f1a\u9047\u5230\u8fd9\u6837\u7684\u95ee\u9898\uff1a\u6211\u4eec\u4e0d\u8fdb\u884c\u725b\u987f\u4e8c\u9879\u5f0f\u5c55\u5f00\u5f0f\uff0c\u800c\u662f\u8981\u6c42\u786e\u5b9a\u725b\u987f\u4e8c\u9879\u5f0f\u7684\u7b2c k \u9879\uff0c\u5373\u5360\u636e\u4f4d\u7f6e k \u7684\u9879\u3002<\/p>\n<p>\u56e0\u6b64\uff0c\u8981\u8ba1\u7b97\u725b\u987f\u4e8c\u9879\u5f0f\u4e2d\u5360\u636e\u4f4d\u7f6e k \u7684\u9879\uff0c\u6211\u4eec\u5fc5\u987b\u4f7f\u7528\u4e00\u4e2a\u516c\u5f0f\uff0c\u8be5\u516c\u5f0f\u53d6\u51b3\u4e8e\u4e8c\u9879\u5f0f\u662f\u52a0\u6cd5\u8fd8\u662f\u51cf\u6cd5\uff1a<\/p>\n<ul style=\"color:#ff5733; font-weight: bold;\">\n<li><span style=\"color:#000000;font-weight: normal;\">\u5982\u679c\u725b\u987f\u4e8c\u9879\u5f0f\u4e3a\u6b63\uff0c\u5219\u7b2c k \u9879\u7684\u503c\u901a\u8fc7\u4ee5\u4e0b\u516c\u5f0f\u8ba1\u7b97\uff1a<\/span><\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-935aea7ee9ad482a391d2383ce37721b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a+b)^n \\quad \\color{red} \\bm{\\longrightarrow} \\color{black} \\quad T_k = \\begin{pmatrix} n \\\\ k-1 \\end{pmatrix} a^{n-k+1}b^{k-1}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"389\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<ul style=\"color:#ff5733; font-weight: bold;\">\n<li><span style=\"color:#000000;font-weight: normal;\">\u5982\u679c\u725b\u987f\u4e8c\u9879\u5f0f\u4e3a\u8d1f\uff0c\u5219\u7b2c k \u9879\u7684\u503c\u7531\u4ee5\u4e0b\u516c\u5f0f\u786e\u5b9a\uff1a<\/span><\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e47024f65b665936296385eae56276af_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a-b)^n \\quad \\color{red} \\bm{\\longrightarrow} \\color{black} \\quad T_k = (-1)^{k-1} \\begin{pmatrix} n \\\\ k-1 \\end{pmatrix} a^{n-k+1} b^{k-1}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"454\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u4f8b\u5982\uff0c\u6211\u4eec\u5c06\u627e\u5230\u4ee5\u4e0b 5 \u6b21\u4e8c\u9879\u5f0f\u7684\u7b2c\u56db\u9879\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c380d61c29b21a0e902b38e390bab73b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x+3)^5\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"61\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u7531\u4e8e\u5b83\u662f\u7531\u548c\u7ec4\u6210\u7684\u4e8c\u9879\u5f0f\uff0c\u56e0\u6b64\u6211\u4eec\u5e94\u7528\u7b2c\u4e00\u4e2a\u516c\u5f0f\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-88faab054915aad2321276aca8b42244_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"T_k = \\begin{pmatrix} n \\\\ k-1 \\end{pmatrix} a^{n-k+1}b^{k-1}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"198\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u6211\u4eec\u5c06\u516c\u5f0f\u4e2d\u7684\u53d8\u91cf\u66ff\u6362\u4e3a\u5176\u5bf9\u5e94\u7684\u503c\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b3b33ca71b5d419c83bb4c5c4b399a69_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"T_4 = \\begin{pmatrix} 5 \\\\ 4-1 \\end{pmatrix} x^{5-4+1}\\cdot 3^{4-1}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"209\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u6211\u4eec\u8fdb\u884c\u4ee5\u4e0b\u64cd\u4f5c\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9dbb0f95e11df6bb989c1a296d168d06_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"T_4 = \\begin{pmatrix} 5 \\\\ 3 \\end{pmatrix} x^{2}\\cdot 3^{3}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"126\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4d566482a87af0eea361c2d7fb816376_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"T_4 = 10 \\cdot x^{2}\\cdot 27\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"121\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9159bbe88a83e38918e8b26354c51db4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"T_4 = 270 x^{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"86\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p>\u8fd9\u6837\u6211\u4eec\u5c31\u8ba1\u7b97\u51fa\u4e86\u725b\u987f\u4e8c\u9879\u5f0f\u5c55\u5f00\u5f0f\u7684\u7b2c\u56db\u9879\uff0c\u800c\u65e0\u9700\u8ba1\u7b97\u6240\u6709\u5176\u4ed6\u9879\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Ejercicios-resueltos-del-binomio-de-Newton\"><\/span>\u89e3\u51b3\u4e86\u725b\u987f\u4e8c\u9879\u5f0f\u7684\u7ec3\u4e60<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u73b0\u5728\u6211\u4eec\u5df2\u7ecf\u89e3\u91ca\u4e86\u4ec0\u4e48\u662f\u4e8c\u9879\u5f0f\u5b9a\u7406\uff0c\u6211\u4eec\u4e3a\u60a8\u63d0\u4f9b\u4e86\u51e0\u4e2a\u6709\u5173\u725b\u987f\u4e8c\u9879\u5f0f\u5b9a\u7406\u7684\u5df2\u89e3\u51b3\u7684\u5206\u6b65\u7ec3\u4e60\uff0c\u4ee5\u4fbf\u60a8\u8fdb\u884c\u7ec3\u4e60\u3002\u53e6\u8bf7\u8bb0\u4f4f\uff0c\u60a8\u53ef\u4ee5\u5728\u8bc4\u8bba\u4e2d\u5411\u6211\u4eec\u7559\u4e0b\u4efb\u4f55\u95ee\u9898\u6216\u5efa\u8bae\u3002<\/p>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e601<\/h3>\n<p>\u4f7f\u7528\u4e8c\u9879\u5f0f\u5b9a\u7406\u5c55\u5f00\u4ee5\u4e0b\u4e8c\u9879\u5f0f\u5e42\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a303d8317c1cf803d486406be48ca672_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x+4)^3\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"61\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__DDF5FF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#DDF5FF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"><strong>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u6211\u4eec\u9996\u5148\u4f7f\u7528\u725b\u987f\u4e8c\u9879\u5f0f\u516c\u5f0f\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-34471d980abe3399791b053ae6b92949_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left(x+4\\right)^3 =\\begin{pmatrix} 3 \\\\ 0 \\end{pmatrix} x^3 \\cdot 4^0 + \\begin{pmatrix} 3 \\\\ 1 \\end{pmatrix} x^{2}\\cdot 4^1 + \\begin{pmatrix} 3 \\\\ 2 \\end{pmatrix} x^{1}\\cdot 4^{2} + \\begin{pmatrix} 3 \\\\ 3 \\end{pmatrix} x^{0}\\cdot 4^{3}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"490\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u7531\u4e8e\u4e8c\u9879\u5f0f\u662f 3 \u6b21\u65b9\uff0c\u6240\u4ee5\u6211\u4eec\u770b\u5854\u5854\u5229\u4e9a\u4e09\u89d2\u5f62\u7684\u7b2c\u4e09\u5c42\uff0c\u76f4\u63a5\u6c42\u7ec4\u5408\u6570\uff1a <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/triangle-de-tartaglia-et-binome-de-newton-ou-pascal.png\" alt=\"\u725b\u987f\u4e8c\u9879\u5f0f\u5b9a\u7406\u7ec3\u4e60\u9898\u4e00\u6b65\u4e00\u6b65\u89e3\u51b31\u9ad8\u4e2d\" class=\"wp-image-2041\" width=\"281\" height=\"192\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8a4212d723eba76e9d883827da60cbfb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x+4)^3 =  1\\cdot x^3 \\cdot 4^0+3 \\cdot x^2 \\cdot 4^1 + 3 \\cdot x^1 \\cdot 4^2+1 \\cdot x^0 \\cdot 4^3\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"425\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u884c\u4f7f\u4ee5\u4e0b\u6743\u529b\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f263aaef5f957165f9d251d4d129038a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"1\\cdot x^3 \\cdot 1 + 3 \\cdot x^2 \\cdot 4+ 3 \\cdot x \\cdot 16 +1 \\cdot 1 \\cdot 64\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"310\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6700\u540e\u6211\u4eec\u4e58\u4ee5\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-dce7abd76ef03c986508c67f59ed4065_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^3  + 3x^2 \\cdot 4 + 3 x \\cdot 16 + 64\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"199\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c0e5d024d22382b1b37a5123547bca3f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{x^3  + 12x^2  + 48 x + 64}\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"164\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e602<\/h3>\n<p>\u7528\u725b\u987f\u4e8c\u9879\u5f0f\u516c\u5f0f\u8ba1\u7b97\u4ee5\u4e0b\u5e42\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f2a2d15ee45a0d9497294d2d4c96b59c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(3x+2)^3\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"70\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__DDF5FF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#DDF5FF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"><strong>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u9996\u5148\uff0c\u6211\u4eec\u5e94\u7528\u725b\u987f\u4e8c\u9879\u5f0f\u516c\u5f0f\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-11acde04483aaa747da0acd16b4912f4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\left(3x+2\\right)^3 =\\begin{pmatrix} 3 \\\\ 0 \\end{pmatrix} (3x)^3 \\cdot 2^0 + \\begin{pmatrix} 3 \\\\ 1 \\end{pmatrix} (3x)^{2}\\cdot 2^1 + \\begin{pmatrix} 3 \\\\ 2 \\end{pmatrix} (3x)^{1}\\cdot 2^{2} + \\begin{pmatrix} 3 \\\\ 3 \\end{pmatrix} (3x)^{0}\\cdot 2^{3}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"589\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u7531\u4e8e\u4e8c\u9879\u5f0f\u662f\u4e09\u6b21\u65b9\uff0c\u6211\u4eec\u770b\u5e15\u65af\u5361\u4e09\u89d2\u5f62\u7684\u7b2c\u4e09\u5c42\u5c31\u53ef\u4ee5\u76f4\u63a5\u77e5\u9053\u7ec4\u5408\u6570\u7684\u503c\uff1a <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/triangle-de-tartaglia-et-binome-de-newton-ou-pascal.png\" alt=\"\u725b\u987f\u4e8c\u9879\u5f0f\u5b9a\u7406\u7ec3\u4e60\u9898\u4e00\u6b65\u4e00\u6b65\u89e3\u51b31\u9ad8\u4e2d\" class=\"wp-image-2041\" width=\"281\" height=\"192\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9086d7be80cd0ba60f0733f2c3a6d042_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left(3x+2\\right)^3 =  1\\cdot  (3x)^3 \\cdot 2^0+3 \\cdot (3x)^2 \\cdot 2^1+ 3 \\cdot (3x)^1 \\cdot 2^2+1 \\cdot (3x)^0 \\cdot 2^3\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"524\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u8ba1\u7b97\u5355\u9879\u5f0f\u7684\u5e42\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2db17751cff5427aa6a3f5da817ba4d3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"1\\cdot  27x^3 \\cdot 1+ 3 \\cdot 9x^2 \\cdot 2+3 \\cdot 3x \\cdot 4 + 1 \\cdot 1 \\cdot 8\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"328\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6700\u540e\uff0c\u6211\u4eec\u8fdb\u884c\u4e58\u6cd5\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-92736e691facfdd97f2107b4451b5d07_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"27x^3  + 27x^2 \\cdot 2 +9x \\cdot 4+8\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"207\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-498bf09ef09e1b2585a5a01193eb94d5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{27x^3  + 54x^2  +36x+8}\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"173\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e603<\/h3>\n<p>\u4f7f\u7528\u725b\u987f\u4e8c\u9879\u5f0f\u516c\u5f0f\u5c55\u5f00\u4ee5\u4e0b\u591a\u9879\u5f0f\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ad4da49317f5a667d4f0402b064911cd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(2x-2)^3\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"70\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__DDF5FF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#DDF5FF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"><strong>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u9996\u5148\uff0c\u6211\u4eec\u4f7f\u7528\u725b\u987f\u4e8c\u9879\u5f0f\u516c\u5f0f\u3002\u4f46\u7531\u4e8e\u62ec\u53f7\u5185\u6709\u51cf\u6cd5\uff0c\u56e0\u6b64\u6211\u4eec\u5fc5\u987b\u4ea4\u6362\u6bcf\u4e00\u9879\u7cfb\u6570\u7684\u7b26\u53f7\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6515c9dadfa92cfcc27393786b322d8c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(2x-2)^3=\\begin{pmatrix} 3 \\\\ 0 \\end{pmatrix} (2x)^3 \\cdot 2^0-\\begin{pmatrix} 3 \\\\ 1 \\end{pmatrix} (2x)^2 \\cdot 2^1 + \\begin{pmatrix} 3 \\\\ 2 \\end{pmatrix} (2x)^1 \\cdot 2^2-\\begin{pmatrix} 3 \\\\ 3 \\end{pmatrix} (2x)^0 \\cdot 2^3\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"589\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u7531\u4e8e\u4e8c\u9879\u5f0f\u662f\u4e09\u6b21\u65b9\uff0c\u6240\u4ee5\u6211\u4eec\u770b\u5854\u5854\u5229\u4e9a\u4e09\u89d2\u5f62\u7684\u7b2c\u4e09\u5c42\u6765\u76f4\u63a5\u8ba1\u7b97\u7ec4\u5408\u6570\uff1a <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/triangle-de-tartaglia-et-binome-de-newton-ou-pascal.png\" alt=\"\u725b\u987f\u4e8c\u9879\u5f0f\u5b9a\u7406\u7ec3\u4e60\u9898\u4e00\u6b65\u4e00\u6b65\u89e3\u51b31\u9ad8\u4e2d\" class=\"wp-image-2041\" width=\"281\" height=\"192\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6d6210b9c330fe976b32741ba8d94682_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(2x-2)^3=1\\cdot  (2x)^3 \\cdot 2^0-3 \\cdot (2x)^2 \\cdot 2^1 + 3 \\cdot (2x)^1 \\cdot 2^2-1 \\cdot (2x)^0 \\cdot 2^3\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"524\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u884c\u4f7f\u4ee5\u4e0b\u6743\u529b\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-25d9bc802e8f03513de309b82066a983_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"1\\cdot  8x^3 \\cdot 1- 3 \\cdot 4 x^2 \\cdot 2+ 3 \\cdot 2x \\cdot 4-1 \\cdot 1 \\cdot 8\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"319\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u89e3\u51b3\u4e58\u6cd5\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5534981aec0ef30054d35f3dd9d9779d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"8x^3  - 12 x^2 \\cdot 2 +6x \\cdot 4 -8\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"199\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-be12e609798d32d7b7c84bae80e04236_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{8x^3  -24 x^2  +24x -8}\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"164\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e604<\/h3>\n<p>\u4f7f\u7528\u4ee5\u4e0b\u516c\u5f0f\u6c42\u4ee5\u4e0b\u725b\u987f\u4e8c\u9879\u5f0f\u7684\u5c55\u5f00\u8868\u8fbe\u5f0f\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6fc4cfe6afa91b302683d9891d785376_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(4x-3y)^4\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"79\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__DDF5FF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#DDF5FF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"><strong>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u6211\u4eec\u5fc5\u987b\u5e94\u7528\u725b\u987f\u4e8c\u9879\u5f0f\u7684\u4e00\u822c\u516c\u5f0f\uff0c\u4f46\u7531\u4e8e\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\u6211\u4eec\u5728\u62ec\u53f7\u4e2d\u8fdb\u884c\u51cf\u6cd5\uff0c\u6240\u4ee5\u6211\u4eec\u5fc5\u987b\u4ea4\u66ff\u6bcf\u4e00\u9879\u7684\u7b26\u53f7\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7a8620bd23846e1f98f7646cbd51dbc5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}(4x-3y)^4 = &amp; \\begin{pmatrix} 4 \\\\ 0 \\end{pmatrix} (4x)^4 \\cdot (3y)^0-\\begin{pmatrix} 4 \\\\ 1 \\end{pmatrix} (4x)^3 \\cdot (3y)^1+\\begin{pmatrix} 4 \\\\ 2 \\end{pmatrix} \\cdot (4x)^2 \\cdot (3y)^2 - \\\\[2ex] &amp; - \\begin{pmatrix} 4 \\\\ 3 \\end{pmatrix}(4x)^1 \\cdot (3y)^3+\\begin{pmatrix} 4 \\\\ 4 \\end{pmatrix}  (4x)^0 \\cdot (3y)^4 \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"109\" width=\"560\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u7531\u4e8e\u4e8c\u9879\u5f0f\u88ab\u63d0\u5347\u5230\u7b2c\u56db\u7ea7\uff0c\u6211\u4eec\u67e5\u770b\u5854\u5854\u5229\u4e9a\u4e09\u89d2\u5f62\u7684\u7b2c 4 \u7ea7\u6765\u76f4\u63a5\u627e\u5230\u7ec4\u5408\u6570\uff1a <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/tirangulo-de-tartaglia-o-pascal-niveau-4.png\" alt=\"\u725b\u987f\u4e8c\u9879\u5f0f\u91d1\u5b57\u5854\" class=\"wp-image-2100\" width=\"296\" height=\"232\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-128e8baa45ddd7d74703c9dfd4a19b06_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}(4x-3y)^4= &amp; \\ 1\\cdot  (4x)^4 \\cdot (3y)^0-4\\cdot  (4x)^3 \\cdot (3y)^1+6 \\cdot (4x)^2 \\cdot (3y)^2 - \\\\[2ex] &amp; - 4 \\cdot (4x)^1 \\cdot (3y)^3+1 \\cdot (4x)^0 \\cdot (3y)^4 \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"504\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u5b9e\u73b0\u4e86\u6240\u6709\u7684\u6743\u529b\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f41577a79066a849e23154b5f55ac638_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"1\\cdot  256x^4 \\cdot 1-4\\cdot  64x^3 \\cdot 3y+6 \\cdot 16x^2 \\cdot 9y^2 - 4 \\cdot 4x \\cdot 27y^3+1 \\cdot 1 \\cdot 81y^4\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"523\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6700\u540e\uff0c\u6211\u4eec\u89e3\u51b3\u4e58\u6cd5\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7790f8c6efcfc885ef79fcecdf89f2af_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"256x^4-256x^3 \\cdot 3y+96x^2 \\cdot 9y^2 - 16x \\cdot 27y^3+81y^4\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"390\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2c9e770e98c445da768bb1371975d48e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{256x^4-768x^3y+864x^2y^2-432xy^3+81y^4}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"334\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e605<\/h3>\n<p>\u786e\u5b9a\u4ee5\u4e0b\u4e8c\u9879\u5f0f\u8868\u8fbe\u5f0f\u5c55\u5f00\u5f0f\u4e2d\u7684\u7b2c\u4e03\u9879\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c76089bd0d5d4f499a0101d91669d461_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(2x-5y)^{10}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"86\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__DDF5FF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#DDF5FF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"><strong>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u7531\u4e8e\u5b83\u662f\u8d1f\u4e8c\u9879\u5f0f\uff0c\u56e0\u6b64\u6211\u4eec\u5fc5\u987b\u4f7f\u7528\u4ee5\u4e0b\u516c\u5f0f\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f27311f76b6e99443d595efdc42e2286_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"T_k = (-1)^{k-1} \\begin{pmatrix} n \\\\ k-1 \\end{pmatrix} a^{n-k+1} b^{k-1}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"263\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u60f3\u8981\u786e\u5b9a\u7b2c7\u9879\uff0c\u5e76\u4e14\u4e8c\u9879\u5f0f\u768410\u6b21\u65b9\uff0c\u56e0\u6b64\u5c06\u8fd9\u4e9b\u503c\u4ee3\u5165\u516c\u5f0f\u5c31\u53d8\u6210\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-65c821f4542af0fe95536ee191c7d430_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"T_7= (-1)^{7-1} \\begin{pmatrix} 10 \\\\ 7-1 \\end{pmatrix} (2x)^{10-7+1} \\cdot (5y)^{7-1}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"326\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c\u4e86\u89e3\u8be5\u672f\u8bed\u5c31\u8db3\u4ee5\u8fdb\u884c\u64cd\u4f5c\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ded0622cbba2bff0563c2f9982c05142_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned} T_7 &amp; = (-1)^{6} \\begin{pmatrix} 10 \\\\ 6 \\end{pmatrix} (2x)^{4} \\cdot (5y)^{6} \\\\[2ex] &amp; = 1 \\cdot 210\\cdot  16x^4 \\cdot 15625y^6 \\\\[2ex] &amp; = \\bm{52500000x^4y^6} \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"129\" width=\"228\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Historia-del-Binomio-de-Newton\"><\/span>\u725b\u987f\u4e8c\u9879\u5f0f\u7684\u5386\u53f2<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u5c3d\u7ba1\u4e8c\u9879\u5f0f\u5b9a\u7406\u7684\u8d77\u6e90\u5f52\u56e0\u4e8e\u82f1\u56fd\u8457\u540d\u79d1\u5b66\u5bb6\u827e\u8428\u514b\u00b7\u725b\u987f\uff08Isaac Newton\uff0c1642-1727\uff09\uff0c\u4f46\u5b9e\u9645\u4e0a\u8be5\u5b9a\u7406\u7684\u7b2c\u4e00\u4e2a\u8868\u8ff0\u662f\u7531\u6ce2\u65af\u5de5\u7a0b\u5e08 Al-Kariji \u5728 1000 \u5e74\u5de6\u53f3\u9996\u6b21\u53d1\u73b0\u7684\uff0c\u751a\u81f3\u8fd8\u53d1\u73b0\uff1a 13\u4e16\u7eaa\uff0c\u4e2d\u56fd\u6570\u5b66\u5bb6\u6768\u8f89\u548c\u6731\u58eb\u6770\u5df2\u7ecf\u77e5\u9053\u5c0f\u6b21\u6570\u7684\u4e8c\u9879\u5f0f\u5c55\u5f00\u5f0f\u3002<\/p>\n<p>\u540e\u6765\uff0c\u5728 17 \u4e16\u7eaa\uff0c\u725b\u987f\u5728\u524d\u4efb\u6570\u5b66\u5bb6\u5960\u5b9a\u7684\u57fa\u7840\u4e0a\u6269\u5c55\u4e86\u4e8c\u9879\u5f0f\u5b9a\u7406\u3002\u5229\u7528\u6570\u5b66\u5bb6\u7ea6\u7ff0\u00b7\u6c83\u5c14\u65af\u7684\u63d2\u503c\u548c\u5916\u63a8\u65b9\u6cd5\u4ee5\u53ca\u5e7f\u4e49\u6307\u6570\u7684\u6982\u5ff5\uff0c\u4ed6\u80fd\u591f\u5c06\u591a\u9879\u5f0f\u8868\u8fbe\u5f0f\u8f6c\u6362\u4e3a\u65e0\u7a77\u7ea7\u6570\u3002<\/p>\n<p> 1665\u5e74\u5de6\u53f3\uff0c\u725b\u987f\u6210\u529f\u8bc1\u660e\u4e86\u4e8c\u9879\u5f0f\u5b9a\u7406\u7684\u6307\u6570n\u4e5f\u53ef\u4ee5\u662f\u6709\u7406\u6307\u6570\uff0c\u4e5f\u5c31\u662f\u8bf4\uff0c\u5982\u679c\u6307\u6570\u662f\u5206\u6570\uff0c\u4e5f\u53ef\u4ee5\u6c42\u89e3\u4e8c\u9879\u5f0f\u7684\u5e42\u3002\u53e6\u4e00\u65b9\u9762\uff0c\u5728\u8d1f\u6307\u6570\u7684\u60c5\u51b5\u4e0b\u4e5f\u5f97\u5230\u4e86\u8bc1\u660e\u3002\u800c\u4e14\uff0c\u4ee4\u4eba\u60ca\u8bb6\u7684\u662f\uff0c\u4ed6\u53d1\u73b0\u8fd9\u4e24\u4e2a\u8868\u8fbe\u5f0f\u7684\u53d1\u5c55\u662f\u9879\u7684\u65e0\u7a77\u7ea7\u6570\u3002<\/p>\n<p>\u6b63\u662f\u6709\u4e86\u8fd9\u4e2a\u53d1\u73b0\uff0c\u725b\u987f\u5f00\u59cb\u8d28\u7591\u65e0\u9650\u7ea7\u6570\u548c\u6709\u9650\u591a\u9879\u5f0f\u8868\u8fbe\u5f0f\u4e4b\u95f4\u7684\u5173\u7cfb\uff0c\u5e76\u63a8\u65ad\u51fa\u65e0\u9650\u7ea7\u6570\u53ef\u4ee5\u50cf\u6709\u9650\u591a\u9879\u5f0f\u8868\u8fbe\u5f0f\u4e00\u6837\u8fdb\u884c\u6570\u5b66\u8fd0\u7b97\u3002\u5c3d\u7ba1\u725b\u987f\u4ece\u672a\u53d1\u8868\u8fc7\u8be5\u5b9a\u7406\uff0c\u4f46\u7ea6\u7ff0\u00b7\u6c83\u5c14\u65af\u6700\u7ec8\u4e8e 1685 \u5e74\u53d1\u8868\u4e86\u8fd9\u4e00\u53d1\u73b0\uff0c\u5e76\u5c06\u8fd9\u4e00\u53d1\u73b0\u5f52\u529f\u4e8e\u725b\u987f\u3002<\/p>\n<div id=\"ezoic-pub-ad-placeholder-176\" data-inserter-version=\"-1\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u5728\u6b64\u9875\u9762\u4e0a\uff0c\u60a8\u5c06\u627e\u5230\u725b\u987f\u4e8c\u9879\u5f0f\uff08\u6216\u4e8c\u9879\u5f0f\u5b9a\u7406\uff09\u53ca\u5176\u516c\u5f0f\u7684\u89e3\u91ca\u3002\u60a8\u8fd8\u53ef\u4ee5\u770b\u5230\u5982\u4f55\u4f7f\u7528\u5854\u5854\u5229\u4e9a\uff08\u6216\u5e15\u65af\u5361\uff09\u4e09\u89d2\u5f62\u6765 &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/cn\/%e4%ba%8c%e9%a1%b9%e5%bc%8f%e6%88%96%e7%89%9b%e9%a1%bf%e4%ba%8c%e9%a1%b9%e5%bc%8f%e5%ae%9a%e7%90%86%e5%85%ac%e5%bc%8f%e5%92%8c%e5%b7%b2%e8%a7%a3%e5%86%b3%e7%9a%84%e7%bb%83%e4%b9%a0\/\"> <span class=\"screen-reader-text\">\u725b\u987f\u4e8c\u9879\u5f0f\uff08\u4e8c\u9879\u5f0f\u5b9a\u7406\uff09<\/span> \u67e5\u770b\u5168\u6587 &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"","footnotes":""},"categories":[2],"tags":[],"class_list":["post-63","post","type-post","status-publish","format-standard","hentry","category-2"],"yoast_head":"<!-- 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