{"id":64,"date":"2023-09-17T07:20:31","date_gmt":"2023-09-17T07:20:31","guid":{"rendered":"https:\/\/mathority.org\/ja\/%e4%ba%8c%e9%a0%85%e3%81%be%e3%81%9f%e3%81%af%e3%83%8b%e3%83%a5%e3%83%bc%e3%83%88%e3%83%b3%e3%81%ae%e4%ba%8c%e9%a0%85%e5%ae%9a%e7%90%86%e3%81%ae%e5%85%ac%e5%bc%8f%e3%81%a8%e6%bc%94%e7%bf%92%e5%95%8f\/"},"modified":"2023-09-17T07:20:31","modified_gmt":"2023-09-17T07:20:31","slug":"%e4%ba%8c%e9%a0%85%e3%81%be%e3%81%9f%e3%81%af%e3%83%8b%e3%83%a5%e3%83%bc%e3%83%88%e3%83%b3%e3%81%ae%e4%ba%8c%e9%a0%85%e5%ae%9a%e7%90%86%e3%81%ae%e5%85%ac%e5%bc%8f%e3%81%a8%e6%bc%94%e7%bf%92%e5%95%8f","status":"publish","type":"post","link":"https:\/\/mathority.org\/ja\/%e4%ba%8c%e9%a0%85%e3%81%be%e3%81%9f%e3%81%af%e3%83%8b%e3%83%a5%e3%83%bc%e3%83%88%e3%83%b3%e3%81%ae%e4%ba%8c%e9%a0%85%e5%ae%9a%e7%90%86%e3%81%ae%e5%85%ac%e5%bc%8f%e3%81%a8%e6%bc%94%e7%bf%92%e5%95%8f\/","title":{"rendered":"\u30cb\u30e5\u30fc\u30c8\u30f3\u306e\u4e8c\u9805 (\u4e8c\u9805\u5b9a\u7406)"},"content":{"rendered":"<p>\u3053\u306e\u30da\u30fc\u30b8\u3067\u306f\u3001\u30cb\u30e5\u30fc\u30c8\u30f3\u306e\u4e8c\u9805\uff08\u307e\u305f\u306f\u4e8c\u9805\u5b9a\u7406\uff09\u3068\u306f\u4f55\u304b\u3001\u305d\u306e\u516c\u5f0f\u306f\u4f55\u306a\u306e\u304b\u306b\u3064\u3044\u3066\u8aac\u660e\u3057\u307e\u3059\u3002\u30bf\u30eb\u30bf\u30fc\u30ea\u30a2 (\u307e\u305f\u306f\u30d1\u30b9\u30ab\u30eb) \u4e09\u89d2\u5f62\u3092\u4f7f\u7528\u3057\u3066\u3053\u308c\u3092\u7c21\u7565\u5316\u3059\u308b\u65b9\u6cd5\u3082\u308f\u304b\u308a\u307e\u3059\u3002\u3055\u3089\u306b\u3001\u30cb\u30e5\u30fc\u30c8\u30f3\u306e\u4e8c\u9805\u5f0f\u3068\u305d\u306e\u3059\u3079\u3066\u306e\u7279\u6027\u3092\u6bb5\u968e\u7684\u306b\u89e3\u304f\u6f14\u7fd2\u3082\u7528\u610f\u3055\u308c\u3066\u3044\u307e\u3059\u3002\u6700\u5f8c\u306b\u3001\u3053\u306e\u975e\u5e38\u306b\u7279\u6b8a\u306a\u5b9a\u7406\u306e\u8d77\u6e90\u306e\u80cc\u5f8c\u306b\u3042\u308b\u8208\u5473\u6df1\u3044\u70b9\u306b\u3064\u3044\u3066\u8aac\u660e\u3057\u307e\u3059\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%C2%BFQue-es-el-binomio-de-Newton\"><\/span>\u30cb\u30e5\u30fc\u30c8\u30f3\u306e\u4e8c\u9805\u5f0f\u3068\u306f\u4f55\u3067\u3059\u304b? <span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p class=\"has-background\" style=\"background-color:#ffebee\">\u6570\u5b66\u3067\u306f\u3001<strong>\u4e8c\u9805\u5b9a\u7406<\/strong>\u3068\u3057\u3066\u3082\u77e5\u3089\u308c\u308b<strong>\u30cb\u30e5\u30fc\u30c8\u30f3\u306e\u4e8c\u9805\u306f<\/strong>\u3001\u4e8c\u9805\u306e\u7d2f\u4e57\u3092\u7c21\u5358\u306b\u8a08\u7b97\u3067\u304d\u308b\u516c\u5f0f\u3067\u3059\u3002\u8a00\u3044\u63db\u3048\u308c\u3070\u3001\u30cb\u30e5\u30fc\u30c8\u30f3\u306e\u4e8c\u9805\u5f0f\u306f\u3001(a+b) \u306e\u5f62\u5f0f\u306e\u4ee3\u6570\u5f0f<sup>\u3092\u89e3\u304f<\/sup>\u3053\u3068\u304c\u3067\u304d\u308b\u516c\u5f0f\u3067\u69cb\u6210\u3055\u308c\u3066\u3044\u307e\u3059\u3002<\/p>\n<p>\u660e\u3089\u304b\u306b\u3001\u3053\u306e\u5b9a\u7406\u306f\u7269\u7406\u5b66\u8005\u3001\u6570\u5b66\u8005\u3001\u54f2\u5b66\u8005\u3067\u3042\u308b\u30a2\u30a4\u30b6\u30c3\u30af \u30cb\u30e5\u30fc\u30c8\u30f3\u537f\u306b\u3061\u306a\u3093\u3067\u547d\u540d\u3055\u308c\u307e\u3057\u305f\u3002\u305f\u3060\u3057\u3001\u3053\u306e\u5b9a\u7406\u304c\u3059\u3067\u306b\u4f7f\u7528\u3055\u308c\u3066\u3044\u305f\u4e2d\u6771\u306e\u6587\u66f8\u304c\u767a\u898b\u3055\u308c\u3066\u3044\u308b\u305f\u3081\u3001\u3053\u306e\u70b9\u306b\u95a2\u3057\u3066\u306f\u3044\u304f\u3064\u304b\u306e\u8b70\u8ad6\u304c\u3042\u308a\u307e\u3059\u3002\u4ee5\u4e0b\u3067\u306f\u3001\u3053\u306e\u6570\u5f0f\u306e\u8d77\u6e90\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u8aac\u660e\u3057\u307e\u3059\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Formula-del-binomio-de-Newton\"><\/span>\u30cb\u30e5\u30fc\u30c8\u30f3\u306e\u4e8c\u9805\u516c\u5f0f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u30cb\u30e5\u30fc\u30c8\u30f3\u306e\u4e8c\u9805\u5f0f\u306e\u5b9a\u7fa9\u3067\u898b\u305f\u3088\u3046\u306b\u3001\u3053\u306e\u5b9a\u7406\u306f\u4e8c\u9805\u5f0f\u306e\u7d2f\u4e57\u3092\u89e3\u304f\u305f\u3081\u306b\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002\u3057\u304b\u3057\u2026\u30cb\u30e5\u30fc\u30c8\u30f3\u306e\u4e8c\u9805\u5f0f\u306f\u3069\u306e\u3088\u3046\u306b\u9069\u7528\u3055\u308c\u308b\u306e\u3067\u3057\u3087\u3046\u304b?\u8a00\u3044\u63db\u3048\u308c\u3070\u3001\u30cb\u30e5\u30fc\u30c8\u30f3\u306e\u4e8c\u9805\u516c\u5f0f\u3068\u306f\u4f55\u3067\u3059\u304b? <\/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>\u30cb\u30e5\u30fc\u30c8\u30f3\u306e\u4e8c\u9805\u5f0f\u306e\u6570\u5b66\u5f0f\u306f<\/strong>\u6b21\u306e\u3068\u304a\u308a\u3067\u3059\u3002<\/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>\u307e\u305f\u306f\u540c\u7b49\u306e\u3082\u306e:<\/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>\u3053\u306e\u516c\u5f0f\u306f\u30cb\u30e5\u30fc\u30c8\u30f3\u306e\u4e8c\u9805\u5f0f\u306e\u6982\u5ff5\u3092\u7406\u89e3\u3059\u308b\u306b\u306f\u5c11\u3057\u8907\u96d1\u306a\u306e\u3067\u3001\u3088\u308a\u3088\u304f\u7406\u89e3\u3067\u304d\u308b\u3088\u3046\u306b\u3001\u4ee5\u4e0b\u306b\u6700\u4f4e\u6b21\u6570\u306e\u4e8c\u9805\u5f0f\u306e\u7d2f\u4e57\u3092\u793a\u3057\u307e\u3059\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\/formule-binomiale-ou-theoreme-de-newton.jpg\" alt=\"\u30cb\u30e5\u30fc\u30c8\u30f3\u306e\u4e8c\u9805\u5b9a\u7406\u306e\u516c\u5f0f\" class=\"wp-image-2126\" width=\"578\" height=\"578\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p>\u3054\u89a7\u306e\u3068\u304a\u308a\u3001\u4e8c\u9805\u5f0f\u3092\u5c55\u958b\u3059\u308b\u3068<strong>\u3001\u7d44\u307f\u5408\u308f\u305b\u6570\u306e\u4e0b\u4f4d\u8981\u7d20\u304c\u5897\u52a0\u3059\u308b\u306e\u3068\u540c\u3058\u3088\u3046\u306b\u3001\u7b2c 1 \u9805 (a) \u306e\u6307\u6570\u304c\u6e1b\u5c11\u3057<\/strong>\u3001<strong>\u7b2c 2 \u9805 (b) \u306e\u6307\u6570\u304c<\/strong>\u5897\u52a0\u3057\u307e\u3059\u3002<\/p>\n<p>\u3057\u305f\u304c\u3063\u3066\u3001\u4e8c\u9805\u5b9a\u7406\u3092\u4f7f\u7528\u3059\u308b\u306b\u306f\u3001\u7d44\u307f\u5408\u308f\u305b\u6570\u3001\u3064\u307e\u308a\u6b21\u306e\u578b\u306e\u4ee3\u6570\u5f0f\u3092\u89e3\u304f\u65b9\u6cd5\u3092\u77e5\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/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\u3057\u305f\u304c\u3063\u3066\u3001\u30cb\u30e5\u30fc\u30c8\u30f3\u4e8c\u9805\u5f0f\u306e\u8a08\u7b97\u65b9\u6cd5\u306e\u4f8b\u3092\u78ba\u8a8d\u3059\u308b\u524d\u306b\u3001\u7d44\u307f\u5408\u308f\u305b\u6570\u3092\u7c21\u5358\u306b\u78ba\u8a8d\u3057\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Numero-combinatorio\"><\/span>\u7d44\u307f\u5408\u308f\u305b\u6570<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong>\u7d44\u307f\u5408\u308f\u305b\u6570<\/strong>(\u307e\u305f\u306f\u4e8c\u9805\u4fc2\u6570) \u3092\u6c7a\u5b9a\u3059\u308b\u306b\u306f\u3001\u6b21\u306e\u5f0f\u3092\u9069\u7528\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/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<\/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>\u305d\u3057\u3066<\/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>\u3053\u308c\u3089\u306f<strong>\u968e\u4e57\u6570<\/strong>\u3067\u3059\u3002\u968e\u4e57\u6570\u306f\u30011 \u304b\u3089\u306a\u308b\u3059\u3079\u3066\u306e\u6b63\u306e\u6574\u6570\u306b\u4e0a\u8a18\u306e\u6570\u3092\u4e57\u7b97\u3059\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u8a08\u7b97\u3055\u308c\u308b\u3053\u3068\u3082\u899a\u3048\u3066\u304a\u3044\u3066\u304f\u3060\u3055\u3044\u3002<\/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>\u4f8b\u3068\u3057\u3066\u3001\u7d44\u307f\u5408\u308f\u305b\u756a\u53f7\u3092\u898b\u3064\u3051\u3066\u3001\u305d\u308c\u304c\u3069\u306e\u3088\u3046\u306b\u884c\u308f\u308c\u308b\u304b\u3092\u78ba\u8a8d\u3057\u307e\u3059\u3002<\/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>\u7d44\u307f\u5408\u308f\u305b\u6570\u5024\u306f\u3001\u30ad\u30fc\u3092\u4f7f\u7528\u3057\u3066\u8a08\u7b97\u6a5f\u3092\u4f7f\u7528\u3057\u3066\u6c7a\u5b9a\u3059\u308b\u3053\u3068\u3082\u3067\u304d\u307e\u3059\u3002 <\/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>\u30cb\u30e5\u30fc\u30c8\u30f3\u4e8c\u9805\u5f0f\u306e\u4f8b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u4e8c\u9805\u5b9a\u7406\u3068\u306f\u4f55\u304b\u3092\u7406\u89e3\u3057\u305f\u3068\u3053\u308d\u3067\u30012 \u3064\u306e\u6570\u5024\u4f8b\u3092\u4f7f\u7528\u3057\u3066\u30cb\u30e5\u30fc\u30c8\u30f3\u306e\u4e8c\u9805\u516c\u5f0f\u3092\u9069\u7528\u3059\u308b\u65b9\u6cd5\u3092\u898b\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n<h3 class=\"wp-block-heading\">\u4f8b1<\/h3>\n<ul>\n<li>\u30cb\u30e5\u30fc\u30c8\u30f3\u306e\u4e8c\u9805\u5f0f\u3092\u9069\u7528\u3057\u3066\u3001\u6b21\u306e\u4e8c\u9805\u5f0f\u306e\u7d2f\u4e57\u3092\u8a08\u7b97\u3057\u307e\u3059\u3002<\/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>\u3082\u3061\u308d\u3093\u3001\u3053\u306e\u4e8c\u9805\u5f0f\u306f 2 \u4e57\u306a\u306e\u3067\u3001\u9855\u8457\u306a\u6052\u7b49\u5f0f\u306e\u516c\u5f0f ( <strong><span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/ja\/\u6052\u7b49\u7a4d-\u6ce8\u76ee\u3059\u3078\u3099\u304d\u7b49\u4fa1\u6027-\u89e3\u6c7a\u6e08\u307f\u6f14\u7fd2\/\">\u9855\u8457\u306a\u6052\u7b49\u5f0f\u306e\u89e3\u304d\u65b9<\/a><\/span><\/strong>) \u3092\u4f7f\u3063\u3066\u89e3\u304f\u3053\u3068\u3082\u3067\u304d\u307e\u3059\u304c\u3001\u4f8b\u3068\u3057\u3066\u4e8c\u9805\u5b9a\u7406\u3092\u4f7f\u7528\u3057\u3066\u8a08\u7b97\u3057\u307e\u3059\u3002<\/p>\n<p>\u307e\u305a\u7b2c\u4e00\u306b\u3001\u30cb\u30e5\u30fc\u30c8\u30f3\u306e\u4e8c\u9805\u516c\u5f0f\u3092\u9069\u7528\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/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>\u3053\u306e\u5834\u5408\u3001n=2 \u3068\u306a\u308b\u305f\u3081\u3001\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/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>\u3088\u304f\u898b\u3066\u304f\u3060\u3055\u3044\u3002\u6700\u521d\u306b\u3001\u6700\u521d\u306e\u9805 (x) \u3092\u53ef\u80fd\u306a\u9650\u308a\u6700\u5927\u5024 (\u3053\u306e\u5834\u5408\u306f 2) \u306b\u5f15\u304d\u4e0a\u3052\u307e\u3059\u3002\u4e00\u65b9\u3001\u7b2c 2 \u9805 (3) \u3092\u53ef\u80fd\u306a\u9650\u308a\u6700\u5c0f\u5024 (\u5e38\u306b 0) \u306b\u5f15\u304d\u4e0a\u3052\u307e\u3059\u3002\u53f3\u306b\u5411\u304b\u3046\u306b\u3064\u308c\u3066\u3001<strong>\u7b2c 1 \u9805\u3092\u4ee5\u524d\u3088\u308a\u3082\u4f4e\u3044\u6570\u5024\u306b<\/strong>\u5f15\u304d\u4e0a\u3052\u3001<strong>\u7b2c 2 \u9805\u3092\u4ee5\u524d\u3088\u308a\u3082\u9ad8\u3044\u6570\u5024\u306b\u5f15\u304d\u4e0a\u3052\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/strong><\/p>\n<p>\u6b21\u306b\u3001\u7d44\u307f\u5408\u308f\u305b\u6570\u5024\u3092\u8a08\u7b97\u3057\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/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>\u529b\u3092\u6c42\u3081\u3066\u89e3\u304d\u307e\u3059\u3002<\/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>\u305d\u3057\u3066\u6700\u5f8c\u306b\u3001\u4e57\u7b97\u3092\u8a08\u7b97\u3057\u307e\u3059\u3002<\/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\">\u4f8b 2<\/h3>\n<p>\u3053\u3053\u3067\u3001\u3082\u3046\u5c11\u3057\u96e3\u3057\u3044\u554f\u984c\u3092\u89e3\u3044\u3066\u307f\u307e\u3059\u3002<\/p>\n<ul>\n<li>\u30cb\u30e5\u30fc\u30c8\u30f3\u306e\u4e8c\u9805\u516c\u5f0f\u3092\u9069\u7528\u3057\u3066\u3001\u6b21\u306e\u4e8c\u9805\u306e\u7d2f\u4e57\u3092\u6c42\u3081\u307e\u3059\u3002<\/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\u9805\u5b9a\u7406\u306e\u516c\u5f0f\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3059\u3002<\/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>\u3053\u306e\u5834\u5408\u3001n=3 \u3068\u306a\u308b\u305f\u3081\u3001\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/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>\u7d44\u307f\u5408\u308f\u305b\u6570\u3092\u8a08\u7b97\u3057\u307e\u3059\u3002<\/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>\u3053\u3053\u3067\u3079\u304d\u4e57\u3092\u89e3\u304d\u307e\u3059\u3002\u3053\u306e\u305f\u3081\u306b\u306f\u3001\u6b21\u306e 2 \u3064\u306e\u30d7\u30ed\u30d1\u30c6\u30a3\u3092\u899a\u3048\u3066\u304a\u304f\u3053\u3068\u304c\u91cd\u8981\u3067\u3059\u3002<\/p>\n<p class=\"has-background\" style=\"background-color:#fffde7\"> \u2022 \u5358\u9805\u5f0f\u3092\u6307\u6570\u5316\u3059\u308b\u3068\u3001\u4fc2\u6570\u3068\u5909\u6570\u3082\u540c\u3058\u6307\u6570\u5316\u3055\u308c\u307e\u3059 \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 \u9805\u3092 0 \u306b\u3059\u308b\u3068 1 \u306b\u306a\u308a\u307e\u3059 \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>\u3057\u305f\u304c\u3063\u3066\u3001\u6b21\u306e 2 \u3064\u306e\u7279\u6027\u3092\u901a\u3058\u3066\u529b\u3092\u6c42\u3081\u307e\u3059\u3002<\/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\u5f8c\u306b\u3001\u9805\u3092\u639b\u3051\u5408\u308f\u305b\u307e\u3059\u3002 <\/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>\u30cb\u30e5\u30fc\u30c8\u30f3\u306e\u4e8c\u9805\u5f0f\u3068\u30bf\u30eb\u30bf\u30fc\u30ea\u30a2 (\u307e\u305f\u306f\u30d1\u30b9\u30ab\u30eb) \u306e\u4e09\u89d2\u5f62<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u4e0a\u306e\u4f8b\u3067\u898b\u305f\u3088\u3046\u306b\u3001\u7d44\u307f\u5408\u308f\u305b\u6570\u5024\u306e\u8a08\u7b97\u306f\u5c11\u3057\u9762\u5012\u3067\u3059\u3002\u30d1\u30b9\u30ab\u30eb\u306e\u4e09\u89d2\u5f62\u3068\u3057\u3066\u3082\u77e5\u3089\u308c\u308b\u30bf\u30eb\u30bf\u30fc\u30ea\u30a2\u306e\u4e09\u89d2\u5f62\u3092\u4f7f\u7528\u3057\u3066\u3001\u305d\u308c\u3089\u306e\u4fa1\u5024\u3092\u76f4\u63a5\u77e5\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u305f\u3081\u3001\u7d44\u307f\u5408\u308f\u305b\u6570\u3092\u89e3\u304f\u5fc5\u8981\u304c\u306a\u3044\u3088\u3046\u306b\u3059\u308b\u305f\u3081\u306e\u30c8\u30ea\u30c3\u30af\u3092\u6559\u3048\u307e\u3059\u3002<\/p>\n<p>\u305d\u308c\u304c\u4f55\u3067\u3042\u308b\u304b\u308f\u304b\u3089\u306a\u3044\u5834\u5408\u306e\u305f\u3081\u306b\u8aac\u660e\u3059\u308b\u3068\u3001<strong>\u30bf\u30eb\u30bf\u30fc\u30ea\u30a2<\/strong><strong>\u306e\u4e09\u89d2\u5f62 (\u30d1\u30b9\u30ab\u30eb\u306e\u4e09\u89d2\u5f62<\/strong>\u3068\u3082\u547c\u3070\u308c\u307e\u3059) \u306f\u3001\u4e09\u89d2\u5f62\u306e\u5f62\u306b\u914d\u7f6e\u3055\u308c\u305f\u6570\u5024\u306e\u6570\u5b66\u7684\u8868\u73fe\u3067\u3059\u3002<\/p>\n<p>\u30bf\u30eb\u30bf\u30fc\u30ea\u30a2\u307e\u305f\u306f\u30d1\u30b9\u30ab\u30eb\u306e\u4e09\u89d2\u5f62\u3092\u4f5c\u6210\u3059\u308b\u306b\u306f\u3001\u4e09\u89d2\u5f62\u306e\u9802\u70b9 (\u5e38\u306b 1) \u304b\u3089\u958b\u59cb\u3057\u3001\u6b21\u306b\u4e0b\u306e\u7dda\u306e\u756a\u53f7\u3092\u6c7a\u5b9a\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u6b21\u306e\u884c\u306e\u5404\u6570\u5024\u306f\u3001\u884c\u306e\u7d42\u7aef\u304c\u5e38\u306b 1 \u3067\u3042\u308b\u5834\u5408\u3092\u9664\u304d\u3001\u305d\u306e\u3059\u3050\u4e0a\u306e 2 \u3064\u306e\u6570\u5024\u306e\u5408\u8a08\u306b\u7b49\u3057\u304f\u306a\u308a\u307e\u3059\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=\"\u30cb\u30e5\u30fc\u30c8\u30f3 \u30da\u30a2 1 \u9ad8\u6821\u30aa\u30f3\u30e9\u30a4\u30f3\" class=\"wp-image-1936\" width=\"220\" height=\"288\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p>\u3057\u305f\u304c\u3063\u3066\u3001\u30bf\u30eb\u30bf\u30fc\u30ea\u30a2\u306e\u4e09\u89d2\u5f62\u306e\u3053\u308c\u3089\u306e\u6570\u5024\u306f\u305d\u308c\u305e\u308c\u3001\u7d44\u307f\u5408\u308f\u305b\u6570\u5024\u306e\u7d50\u679c\u306b\u5bfe\u5fdc\u3057\u307e\u3059\u3002\u6b21\u306e\u56f3\u3092\u898b\u3066\u304f\u3060\u3055\u3044\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\/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>\u305f\u3068\u3048\u3070\u3001\u4e8c\u9805\u4fc2\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>\u30bf\u30eb\u30bf\u30fc\u30ea\u30a2\u306e\u4e09\u89d2\u5f62\u3067\u306f\u305d\u306e\u4f4d\u7f6e\u306b 3 \u304c\u3042\u308b\u305f\u3081\u3001 \u306f 3 \u306b\u76f8\u5f53\u3057\u307e\u3059\u3002<\/p>\n<p>\u3057\u305f\u304c\u3063\u3066\u3001\u30bf\u30eb\u30bf\u30fc\u30ea\u30a2 (\u307e\u305f\u306f\u30d1\u30b9\u30ab\u30eb) \u306e\u4e09\u89d2\u5f62\u3092\u4f7f\u7528\u3059\u308b\u3068\u3001\u7d44\u307f\u5408\u308f\u305b\u6570\u306e\u8a08\u7b97\u304c\u4e0d\u8981\u306b\u306a\u308b\u305f\u3081\u3001\u30cb\u30e5\u30fc\u30c8\u30f3\u306e\u4e8c\u9805\u5f0f\u3092\u3088\u308a\u8fc5\u901f\u306b\u89e3\u304f\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>\u305f\u3068\u3048\u3070\u3001\u6b21\u306e\u3088\u3046\u306a\u4e8c\u9805\u5f0f\u306e\u5897\u5f37\u3092\u884c\u3044\u305f\u3044\u5834\u5408:<\/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>\u30cb\u30e5\u30fc\u30c8\u30f3\u306e\u4e8c\u9805\u5247\u3092\u9069\u7528\u3059\u308b\u3068\u3001\u6b21\u306e\u4ee3\u6570\u5f0f\u304c\u5f97\u3089\u308c\u307e\u3059\u3002<\/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>\u7d44\u307f\u5408\u308f\u305b\u6570\u3092 1 \u3064\u305a\u3064\u8a08\u7b97\u3059\u308b\u4ee3\u308f\u308a\u306b\u3001\u5404\u7d44\u307f\u5408\u308f\u305b\u6570\u3092\u5bfe\u5fdc\u3059\u308b\u30bf\u30eb\u30bf\u30fc\u30ea\u30a2\u4e09\u89d2\u5f62\u306e\u4fc2\u6570\u306b\u7f6e\u304d\u63db\u3048\u308b\u3060\u3051\u3067\u6e08\u307f\u307e\u3059\u3002\u3053\u306e\u5834\u5408\u3001\u4e8c\u9805\u5f0f\u306f 3 \u756a\u76ee\u307e\u3067\u5f15\u304d\u4e0a\u3052\u3089\u308c\u308b\u305f\u3081\u3001\u4e09\u89d2\u5f62\u306e 3 \u756a\u76ee\u306e\u30ec\u30d9\u30eb\u306b\u5bfe\u5fdc\u3057\u307e\u3059\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\/triangle-de-tartaglia-et-binome-de-newton-ou-pascal.png\" alt=\"\u30bf\u30eb\u30bf\u30fc\u30ea\u30a2\u307e\u305f\u306f\u30d1\u30b9\u30ab\u30eb\u306e\u4e09\u89d2\u5f62\u3068\u30cb\u30e5\u30fc\u30c8\u30f3\u306e\u4e8c\u9805\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>\u3042\u3068\u306f\u6b8b\u308a\u306e\u64cd\u4f5c\u3092\u884c\u3046\u3060\u3051\u3067\u3059\u3002<\/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>\u3054\u89a7\u306e\u3068\u304a\u308a\u3001\u30bf\u30eb\u30bf\u30fc\u30ea\u30a2 (\u307e\u305f\u306f\u30d1\u30b9\u30ab\u30eb) \u306e\u4e09\u89d2\u5f62\u306f\u3001\u3053\u308c\u307e\u3067\u306b\u793a\u3057\u305f\u3088\u3046\u306b\u3001\u3088\u308a\u7c21\u5358\u304b\u3064\u9ad8\u901f\u306a\u65b9\u6cd5\u3067\u30cb\u30e5\u30fc\u30c8\u30f3\u306e\u4e8c\u9805\u5f0f\u3092\u8a08\u7b97\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002\u3053\u306e\u305f\u3081\u3001\u3053\u308c\u3092\u4f7f\u7528\u3059\u308b\u3053\u3068\u3092\u304a\u52e7\u3081\u3057\u307e\u3059\u3002<\/p>\n<p class=\"has-text-align-left\">\u3053\u308c\u307e\u3067\u306b\u898b\u3066\u304d\u305f\u3053\u3068\u3092\u8981\u7d04\u3059\u308b\u305f\u3081\u306b\u3001\u30bf\u30eb\u30bf\u30fc\u30ea\u30a2 (\u307e\u305f\u306f\u30d1\u30b9\u30ab\u30eb) \u4e09\u89d2\u5f62\u306e\u6570\u3092\u4f7f\u7528\u3057\u305f\u30cb\u30e5\u30fc\u30c8\u30f3\u306e\u4e8c\u9805\u5f0f\u306e\u5f0f\u304c\u3069\u306e\u3088\u3046\u306a\u3082\u306e\u304b\u3092\u793a\u3059\u753b\u50cf\u3092\u793a\u3057\u307e\u3059\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\/binome-de-newton-et-triangle-de-pascal-ou-de-tartaglia-2.jpg\" alt=\"\u30cb\u30e5\u30fc\u30c8\u30f3\u306e\u4e8c\u9805\u5f0f\u3068\u30d1\u30b9\u30ab\u30eb\u306e\u4e09\u89d2\u5f62\u307e\u305f\u306f\u30bf\u30eb\u30bf\u30fc\u30ea\u30a2\" 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>\u8ca0\u306e\u30cb\u30e5\u30fc\u30c8\u30f3\u4e8c\u9805\u5f0f: \u6e1b\u7b97\u306e\u7d2f\u4e57<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u3053\u308c\u307e\u3067\u306e\u3068\u3053\u308d\u3001\u79c1\u305f\u3061\u304c\u89e3\u3044\u305f\u30cb\u30e5\u30fc\u30c8\u30f3\u306e\u4e8c\u9805\u5f0f\u306e\u4f8b\u306f\u3059\u3079\u3066\u52a0\u7b97\u3067\u3057\u305f\u3002\u4e00\u65b9\u3001\u4e8c\u9805\u5f0f\u306e 2 \u3064\u306e\u9805\u306e\u3046\u3061\u306e 1 \u3064\u304c\u8ca0\u306e\u7b26\u53f7\u3092\u6301\u3064\u5834\u5408\u3001\u624b\u9806\u306f\u540c\u69d8\u3067\u3059\u304c\u3001\u5c11\u3057\u7570\u306a\u308a\u307e\u3059\u3002<\/p>\n<p class=\"has-background\" style=\"background-color:#ffebee\">\u4e8c\u9805\u5f0f\u306e\u9805\u306e 1 \u3064\u304c\u8ca0\u3067\u3042\u308b\u5834\u5408\u3001\u3064\u307e\u308a (ab) <sup>n<\/sup>\u578b\u306e\u6e1b\u7b97\u3067\u3042\u308b\u5834\u5408\u3001\u30cb\u30e5\u30fc\u30c8\u30f3\u4e8c\u9805\u5f0f\u306e\u5c55\u958b\u306e\u7b26\u53f7\u306f + \u2013 + \u2013 + \u2013 + \u2013 \u2026 \u306e\u5f62\u5f0f\u3067\u4ea4\u4e92\u306b\u4ee3\u308f\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<p>\u4ee5\u4e0b\u3067\u306f\u3001\u4e8c\u9805\u5b9a\u7406\u3068\u3059\u3067\u306b\u8a2d\u5b9a\u3055\u308c\u3066\u3044\u308b\u30bf\u30eb\u30bf\u30fc\u30ea\u30a2\u4e09\u89d2\u5f62\u306e\u4fc2\u6570\u3092\u4f7f\u7528\u3057\u3066\u3001\u6700\u521d\u306e 5 \u6b21\u306e\u8ca0\u306e\u4e8c\u9805\u306e\u7d2f\u4e57\u3092\u5c55\u958b\u3057\u3066\u3044\u307e\u3059\u3002\u3053\u308c\u306b\u3088\u308a\u3001\u5fc5\u8981\u306a\u4e8c\u9805\u5f0f\u3092\u76f4\u63a5\u898b\u3064\u3051\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\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\/puissance-binomiale-newton-negative-dune-soustraction-2.jpg\" alt=\"\u6e1b\u7b97\u306e\u8ca0\u306e\u30cb\u30e5\u30fc\u30c8\u30f3\u4e8c\u9805\u7d2f\u4e57 2\" 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>\u30cb\u30e5\u30fc\u30c8\u30f3\u4e8c\u9805\u5f0f\u306e\u6027\u8cea<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u30cb\u30e5\u30fc\u30c8\u30f3\u306e\u4e8c\u9805\u5f0f\u306b\u306f\u6b21\u306e\u7279\u5fb4\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\u30cb\u30e5\u30fc\u30c8\u30f3\u306e\u4e8c\u9805\u5f0f\u3092\u5206\u89e3\u3059\u308b\u3068\u3001\u5e38\u306b\u4e8c\u9805\u5f0f\u306e\u6b21\u6570\u3088\u308a\u3082 1 \u3064\u306e\u9805\u304c\u591a\u304f\u306a\u308a\u307e\u3059\u3002\u8a00\u3044\u63db\u3048\u308c\u3070\u3001\u30da\u30a2\u306b\u3068\u3063\u3066\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>\u5f7c\u3089\u306f\u5f71\u97ff\u3092\u53d7\u3051\u3066\u3044\u307e\u3059<\/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\u9805\u3002<\/li>\n<li>\u30a8\u30ec\u30e1\u30f3\u30c8\u306e\u529b\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>\u76ae\u5207\u308a\u306b<\/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>\u305d\u3057\u3066\u6700\u5f8c\u306e\u56db\u534a\u671f\u3067 0 \u306b\u306a\u308b\u307e\u3067\u6e1b\u5c11\u3057\u307e\u3059\u3002<\/li>\n<li>\u30a8\u30ec\u30e1\u30f3\u30c8\u306e\u529b\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>\u305d\u308c\u3089\u306f\u53cd\u5bfe\u65b9\u5411\u306b\u9032\u307f\u307e\u3059\u30020 \u304b\u3089\u59cb\u307e\u308a\u30010 \u306b\u9054\u3059\u308b\u307e\u3067\u5897\u52a0\u3057\u307e\u3059\u3002<\/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>\u6700\u5f8c\u306e\u5b66\u671f\u306b\u3002<\/li>\n<li>\u30cb\u30e5\u30fc\u30c8\u30f3\u306e\u4e8c\u9805\u5f0f\u306e\u5404\u8981\u7d20\u306b\u3064\u3044\u3066\u3001\u6b21\u306e\u6307\u6570\u306e\u5408\u8a08\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>\u305d\u3057\u3066<\/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>\u306b\u7b49\u3057\u3044<\/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>\u30cb\u30e5\u30fc\u30c8\u30f3\u306e\u4e8c\u9805\u5f0f\u306e\u6700\u521d\u306e\u9805\u306e\u4fc2\u6570\u306f\u5e38\u306b 1 (\u6b63) \u3067\u30012 \u756a\u76ee\u306e\u4fc2\u6570\u306f\u4e8c\u9805\u5f0f\u306e\u6307\u6570 (\u6b63\u307e\u305f\u306f\u8ca0) \u306b\u76f8\u5f53\u3057\u307e\u3059\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>\u30cb\u30e5\u30fc\u30c8\u30f3\u4e8c\u9805\u5f0f\u306e k \u756a\u76ee\u306e\u9805\u3092\u8a08\u7b97\u3057\u307e\u3059<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u3053\u308c\u306f\u73cd\u3057\u3044\u3053\u3068\u3067\u3059\u304c\u3001\u30cb\u30e5\u30fc\u30c8\u30f3\u306e\u4e8c\u9805\u5c55\u958b\u3092\u884c\u3046\u4ee3\u308f\u308a\u306b\u3001\u30cb\u30e5\u30fc\u30c8\u30f3\u306e\u4e8c\u9805\u5f0f\u306e k \u756a\u76ee\u306e\u9805\u3001\u3064\u307e\u308a k \u306e\u4f4d\u7f6e\u3092\u5360\u3081\u308b\u9805\u3092\u6c7a\u5b9a\u3059\u308b\u5fc5\u8981\u304c\u3042\u308b\u3068\u3044\u3046\u554f\u984c\u306b\u906d\u9047\u3059\u308b\u3053\u3068\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<p>\u3057\u305f\u304c\u3063\u3066\u3001\u30cb\u30e5\u30fc\u30c8\u30f3\u306e\u4e8c\u9805\u5f0f\u306e k \u306e\u4f4d\u7f6e\u3092\u5360\u3081\u308b\u9805\u3092\u8a08\u7b97\u3059\u308b\u306b\u306f\u3001\u4e8c\u9805\u5f0f\u304c\u52a0\u7b97\u3067\u3042\u308b\u304b\u6e1b\u7b97\u3067\u3042\u308b\u304b\u306b\u5fdc\u3058\u3066\u6b21\u306e\u5f0f\u3092\u4f7f\u7528\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<ul style=\"color:#ff5733; font-weight: bold;\">\n<li><span style=\"color:#000000;font-weight: normal;\">\u30cb\u30e5\u30fc\u30c8\u30f3\u306e\u4e8c\u9805\u5f0f\u304c\u6b63\u306e\u5834\u5408\u3001k \u756a\u76ee\u306e\u9805\u306e\u5024\u306f\u6b21\u306e\u5f0f\u3067\u8a08\u7b97\u3055\u308c\u307e\u3059\u3002<\/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;\">\u30cb\u30e5\u30fc\u30c8\u30f3\u306e\u4e8c\u9805\u5f0f\u304c\u8ca0\u306e\u5834\u5408\u3001k \u756a\u76ee\u306e\u9805\u306e\u5024\u306f\u6b21\u306e\u5f0f\u3067\u6c7a\u5b9a\u3055\u308c\u307e\u3059\u3002<\/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\u3068\u3057\u3066\u3001\u6b21\u306e 5 \u6b21\u306e\u4e8c\u9805\u5f0f\u306e\u7b2c 4 \u9805\u3092\u898b\u3064\u3051\u307e\u3059\u3002<\/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>\u3053\u308c\u306f\u5408\u8a08\u3067\u69cb\u6210\u3055\u308c\u308b\u4e8c\u9805\u306a\u306e\u3067\u3001\u6700\u521d\u306e\u5f0f\u3092\u9069\u7528\u3057\u307e\u3059\u3002<\/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>\u5f0f\u5185\u306e\u5909\u6570\u3092\u5bfe\u5fdc\u3059\u308b\u5024\u306b\u7f6e\u304d\u63db\u3048\u307e\u3059\u3002<\/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>\u305d\u3057\u3066\u3001\u6b21\u306e\u64cd\u4f5c\u3092\u5b9f\u884c\u3057\u307e\u3059\u3002 <\/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>\u3053\u306e\u3088\u3046\u306b\u3057\u3066\u3001\u4ed6\u306e\u3059\u3079\u3066\u306e\u9805\u3092\u8a08\u7b97\u3059\u308b\u5fc5\u8981\u306a\u304f\u3001\u30cb\u30e5\u30fc\u30c8\u30f3\u306e\u4e8c\u9805\u5c55\u958b\u306e\u7b2c 4 \u9805\u3092\u8a08\u7b97\u3057\u307e\u3057\u305f\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Ejercicios-resueltos-del-binomio-de-Newton\"><\/span>\u30cb\u30e5\u30fc\u30c8\u30f3\u306e\u4e8c\u9805\u5f0f\u306e\u6f14\u7fd2\u554f\u984c\u3092\u89e3\u6c7a\u3057\u307e\u3057\u305f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u4e8c\u9805\u5b9a\u7406\u3068\u306f\u4f55\u304b\u3092\u8aac\u660e\u3057\u305f\u3068\u3053\u308d\u3067\u3001\u30cb\u30e5\u30fc\u30c8\u30f3\u306e\u4e8c\u9805\u5b9a\u7406\u306b\u95a2\u3059\u308b\u6bb5\u968e\u7684\u306a\u6f14\u7fd2\u3092\u3044\u304f\u3064\u304b\u7528\u610f\u3057\u3066\u3001\u7df4\u7fd2\u3067\u304d\u308b\u3088\u3046\u306b\u3057\u307e\u3059\u3002\u307e\u305f\u3001\u3054\u8cea\u554f\u3084\u3054\u63d0\u6848\u304c\u3054\u3056\u3044\u307e\u3057\u305f\u3089\u3001\u30b3\u30e1\u30f3\u30c8\u6b04\u306b\u6b8b\u3057\u3066\u3044\u305f\u3060\u3051\u307e\u3059\u3088\u3046\u304a\u9858\u3044\u3044\u305f\u3057\u307e\u3059\u3002<\/p>\n<h3 class=\"wp-block-heading\">\u6f14\u7fd2 1<\/h3>\n<p>\u4e8c\u9805\u5b9a\u7406\u3092\u4f7f\u7528\u3057\u3066\u6b21\u306e\u4e8c\u9805\u7d2f\u4e57\u3092\u5c55\u958b\u3057\u307e\u3059\u3002 <\/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>\u89e3\u6c7a\u7b56\u3092\u898b\u308b<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u307e\u305a\u30cb\u30e5\u30fc\u30c8\u30f3\u306e\u4e8c\u9805\u516c\u5f0f\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002<\/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\">\u4e8c\u9805\u5f0f\u306f 3 \u4e57\u3055\u308c\u308b\u305f\u3081\u3001\u30bf\u30eb\u30bf\u30fc\u30ea\u30a2\u4e09\u89d2\u5f62\u306e 3 \u756a\u76ee\u306e\u30ec\u30d9\u30eb\u3092\u8abf\u3079\u3066\u3001\u7d44\u307f\u5408\u308f\u305b\u6570\u3092\u76f4\u63a5\u898b\u3064\u3051\u307e\u3059\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\/triangle-de-tartaglia-et-binome-de-newton-ou-pascal.png\" alt=\"\u30cb\u30e5\u30fc\u30c8\u30f3\u306e\u4e8c\u9805\u5b9a\u7406\u306e\u6f14\u7fd2\u3092\u6bb5\u968e\u7684\u306b\u89e3\u304f \u9ad8\u6821 1\" 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\">\u79c1\u305f\u3061\u306f\u6b21\u306e\u6a29\u9650\u3092\u5b9f\u884c\u3057\u307e\u3059\u3002<\/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\">\u305d\u3057\u3066\u6700\u5f8c\u306b\u6b21\u306e\u3088\u3046\u306b\u4e57\u7b97\u3057\u307e\u3059\u3002 <\/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\">\u6f14\u7fd2 2<\/h3>\n<p>\u30cb\u30e5\u30fc\u30c8\u30f3\u306e\u4e8c\u9805\u516c\u5f0f\u3092\u4f7f\u7528\u3057\u3066\u6b21\u306e\u3079\u304d\u4e57\u3092\u8a08\u7b97\u3057\u307e\u3059\u3002 <\/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>\u89e3\u6c7a\u7b56\u3092\u898b\u308b<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u307e\u305a\u3001\u30cb\u30e5\u30fc\u30c8\u30f3\u306e\u4e8c\u9805\u516c\u5f0f\u3092\u9069\u7528\u3057\u307e\u3059\u3002<\/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\">\u4e8c\u9805\u5f0f\u306f 3 \u4e57\u306a\u306e\u3067\u3001\u7d44\u307f\u5408\u308f\u305b\u6570\u306e\u5024\u3092\u76f4\u63a5\u77e5\u308b\u305f\u3081\u306b\u30d1\u30b9\u30ab\u30eb\u306e\u4e09\u89d2\u5f62\u306e 3 \u756a\u76ee\u306e\u30ec\u30d9\u30eb\u3092\u8abf\u3079\u307e\u3059\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\/triangle-de-tartaglia-et-binome-de-newton-ou-pascal.png\" alt=\"\u30cb\u30e5\u30fc\u30c8\u30f3\u306e\u4e8c\u9805\u5b9a\u7406\u306e\u6f14\u7fd2\u3092\u6bb5\u968e\u7684\u306b\u89e3\u304f \u9ad8\u6821 1\" 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\">\u5358\u9805\u5f0f\u306e\u7d2f\u4e57\u3092\u8a08\u7b97\u3057\u307e\u3059\u3002<\/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\">\u305d\u3057\u3066\u6700\u5f8c\u306b\u3001\u4e57\u7b97\u3092\u5b9f\u884c\u3057\u307e\u3059\u3002 <\/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\">\u6f14\u7fd2 3<\/h3>\n<p>\u30cb\u30e5\u30fc\u30c8\u30f3\u306e\u4e8c\u9805\u516c\u5f0f\u3092\u4f7f\u7528\u3057\u3066\u6b21\u306e\u591a\u9805\u5f0f\u3092\u5c55\u958b\u3057\u307e\u3059\u3002 <\/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>\u89e3\u6c7a\u7b56\u3092\u898b\u308b<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u307e\u305a\u3001\u30cb\u30e5\u30fc\u30c8\u30f3\u306e\u4e8c\u9805\u516c\u5f0f\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002\u305f\u3060\u3057\u3001\u62ec\u5f27\u5185\u306b\u6e1b\u7b97\u304c\u3042\u308b\u305f\u3081\u3001\u5404\u9805\u306e\u4fc2\u6570\u306e\u7b26\u53f7\u3092\u4ea4\u4e92\u306b\u5207\u308a\u66ff\u3048\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/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\">\u4e8c\u9805\u5f0f\u306f 3 \u4e57\u3055\u308c\u308b\u305f\u3081\u3001\u30bf\u30eb\u30bf\u30fc\u30ea\u30a2\u4e09\u89d2\u5f62\u306e 3 \u756a\u76ee\u306e\u30ec\u30d9\u30eb\u3092\u8abf\u3079\u3066\u3001\u7d44\u307f\u5408\u308f\u305b\u6570\u3092\u76f4\u63a5\u8a08\u7b97\u3057\u307e\u3059\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\/triangle-de-tartaglia-et-binome-de-newton-ou-pascal.png\" alt=\"\u30cb\u30e5\u30fc\u30c8\u30f3\u306e\u4e8c\u9805\u5b9a\u7406\u306e\u6f14\u7fd2\u3092\u6bb5\u968e\u7684\u306b\u89e3\u304f \u9ad8\u6821 1\" 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\">\u79c1\u305f\u3061\u306f\u6b21\u306e\u6a29\u9650\u3092\u5b9f\u884c\u3057\u307e\u3059\u3002<\/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\">\u305d\u3057\u3066\u4e57\u7b97\u3092\u89e3\u304d\u307e\u3059\u3002 <\/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\">\u6f14\u7fd2 4<\/h3>\n<p>\u6b21\u306e\u5f0f\u3092\u4f7f\u7528\u3057\u3066\u3001\u6b21\u306e\u30cb\u30e5\u30fc\u30c8\u30f3\u4e8c\u9805\u5f0f\u306e\u5c55\u958b\u5f0f\u3092\u6c42\u3081\u307e\u3059\u3002 <\/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>\u89e3\u6c7a\u7b56\u3092\u898b\u308b<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u30cb\u30e5\u30fc\u30c8\u30f3\u306e\u4e8c\u9805\u5f0f\u306e\u4e00\u822c\u5f0f\u3092\u9069\u7528\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u304c\u3001\u3053\u306e\u5834\u5408\u306f\u62ec\u5f27\u5185\u306b\u6e1b\u7b97\u304c\u3042\u308b\u305f\u3081\u3001\u5404\u9805\u306e\u7b26\u53f7\u3092\u4ea4\u4e92\u306b\u914d\u7f6e\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/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\">\u4e8c\u9805\u5f0f\u304c 4 \u756a\u76ee\u306b\u5f15\u304d\u4e0a\u3052\u3089\u308c\u308b\u305f\u3081\u3001\u30bf\u30eb\u30bf\u30fc\u30ea\u30a2\u4e09\u89d2\u5f62\u306e\u30ec\u30d9\u30eb 4 \u3092\u898b\u3066\u3001\u7d44\u307f\u5408\u308f\u305b\u6570\u3092\u76f4\u63a5\u898b\u3064\u3051\u307e\u3059\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\/tirangulo-de-tartaglia-o-pascal-niveau-4.png\" alt=\"\u30cb\u30e5\u30fc\u30c8\u30f3\u306e\u4e8c\u9805\u30d4\u30e9\u30df\u30c3\u30c9\" 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\">\u79c1\u305f\u3061\u306f\u3059\u3079\u3066\u306e\u529b\u3092\u8a8d\u8b58\u3057\u3066\u3044\u307e\u3059\u3002<\/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\">\u305d\u3057\u3066\u6700\u5f8c\u306b\u3001\u4e57\u7b97\u3092\u89e3\u304d\u307e\u3059\u3002 <\/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\">\u6f14\u7fd2 5<\/h3>\n<p>\u6b21\u306e\u4e8c\u9805\u5f0f\u306e\u5c55\u958b\u306e 7 \u756a\u76ee\u306e\u9805\u3092\u6c7a\u5b9a\u3057\u307e\u3059\u3002 <\/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>\u89e3\u6c7a\u7b56\u3092\u898b\u308b<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u3053\u308c\u306f\u8ca0\u306e\u4e8c\u9805\u306a\u306e\u3067\u3001\u6b21\u306e\u5f0f\u3092\u4f7f\u7528\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/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\">\u9805 7 \u3092\u6c7a\u5b9a\u3057\u305f\u3044\u306e\u3067\u3059\u304c\u3001\u4e8c\u9805\u5f0f\u306f 10 \u4e57\u3055\u308c\u308b\u305f\u3081\u3001\u5f0f\u306b\u5024\u3092\u4ee3\u5165\u3059\u308b\u3068\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/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\">\u3057\u305f\u304c\u3063\u3066\u3001\u6b21\u306e\u7528\u8a9e\u3092\u7406\u89e3\u3059\u308b\u306b\u306f\u64cd\u4f5c\u3092\u884c\u3046\u3060\u3051\u3067\u5341\u5206\u3067\u3059\u3002 <\/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>\u30cb\u30e5\u30fc\u30c8\u30f3\u306e\u4e8c\u9805\u5f0f\u306e\u6b74\u53f2<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u4e8c\u9805\u5b9a\u7406\u306e\u8d77\u6e90\u306f\u6709\u540d\u306a\u30a4\u30ae\u30ea\u30b9\u306e\u79d1\u5b66\u8005\u30a2\u30a4\u30b6\u30c3\u30af \u30cb\u30e5\u30fc\u30c8\u30f3 (1642-1727) \u306b\u3088\u308b\u3082\u306e\u3068\u3055\u308c\u3066\u3044\u307e\u3059\u304c\u3001\u5b9f\u969b\u306b\u306f\u3001\u3053\u306e\u5b9a\u7406\u306e\u6700\u521d\u306e\u5b9a\u5f0f\u5316\u306f 1000 \u5e74\u9803\u306b\u30da\u30eb\u30b7\u30e3\u306e\u6280\u8853\u8005\u30a2\u30eb \u30ab\u30ea\u30b8\u30fc\u306b\u3088\u3063\u3066\u521d\u3081\u3066\u767a\u898b\u3055\u308c\u307e\u3057\u305f\u3002 13 \u4e16\u7d00\u306b\u306f\u3001\u4e2d\u56fd\u306e\u6570\u5b66\u8005\u694a\u8f1d\u3068\u6731\u4e16\u5091\u306f\u3059\u3067\u306b\u5c0f\u3055\u306a\u6b21\u6570\u306e\u4e8c\u9805\u5c55\u958b\u3092\u77e5\u3063\u3066\u3044\u307e\u3057\u305f\u3002<\/p>\n<p>\u305d\u306e\u5f8c 17 \u4e16\u7d00\u306b\u3001\u30cb\u30e5\u30fc\u30c8\u30f3\u306f\u4ee5\u524d\u306e\u6570\u5b66\u8005\u304c\u7bc9\u3044\u305f\u57fa\u790e\u3092\u57fa\u790e\u306b\u3057\u3066\u4e8c\u9805\u5b9a\u7406\u3092\u62e1\u5f35\u3057\u307e\u3057\u305f\u3002\u6570\u5b66\u8005\u30b8\u30e7\u30f3 \u30a6\u30a9\u30fc\u30eb\u30ba\u306e\u5185\u633f\u3068\u5916\u633f\u306e\u65b9\u6cd5\u3001\u304a\u3088\u3073\u4e00\u822c\u5316\u6307\u6570\u306e\u6982\u5ff5\u3092\u4f7f\u7528\u3057\u3066\u3001\u5f7c\u306f\u591a\u9805\u5f0f\u3092\u7121\u9650\u7d1a\u6570\u306b\u5909\u63db\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u3002<\/p>\n<p> 1665 \u5e74\u9803\u3001\u30cb\u30e5\u30fc\u30c8\u30f3\u306f\u3001\u4e8c\u9805\u5b9a\u7406\u306e\u6307\u6570 n \u304c\u6709\u7406\u6307\u6570\u306b\u306a\u308a\u5f97\u308b\u3053\u3068\u3001\u3064\u307e\u308a\u3001\u6307\u6570\u304c\u5206\u6570\u306e\u5834\u5408\u306b\u3082\u4e8c\u9805\u7d2f\u4e57\u3092\u89e3\u304f\u3053\u3068\u304c\u3067\u304d\u308b\u3053\u3068\u3092\u8a3c\u660e\u3059\u308b\u3053\u3068\u306b\u6210\u529f\u3057\u307e\u3057\u305f\u3002\u4e00\u65b9\u3001\u8ca0\u306e\u6307\u6570\u306e\u5834\u5408\u3067\u3082\u8a3c\u660e\u3055\u308c\u307e\u3057\u305f\u3002\u305d\u3057\u3066\u9a5a\u304f\u3079\u304d\u3053\u3068\u306b\u3001\u5f7c\u306f 2 \u3064\u306e\u5f0f\u306e\u5c55\u958b\u304c\u9805\u306e\u7121\u9650\u7d1a\u6570\u3067\u3042\u308b\u3053\u3068\u3092\u767a\u898b\u3057\u307e\u3057\u305f\u3002<\/p>\n<p>\u3053\u306e\u767a\u898b\u3092\u304d\u3063\u304b\u3051\u306b\u3001\u30cb\u30e5\u30fc\u30c8\u30f3\u306f\u7121\u9650\u7d1a\u6570\u3068\u6709\u9650\u591a\u9805\u5f0f\u306e\u95a2\u4fc2\u306b\u7591\u554f\u3092\u6301\u3061\u59cb\u3081\u3001\u7121\u9650\u7d1a\u6570\u3067\u3082\u6709\u9650\u591a\u9805\u5f0f\u3068\u540c\u3058\u3088\u3046\u306b\u6570\u5b66\u7684\u306a\u6f14\u7b97\u304c\u5b9f\u884c\u3067\u304d\u308b\u3068\u63a8\u6e2c\u3057\u307e\u3057\u305f\u3002\u30cb\u30e5\u30fc\u30c8\u30f3\u306f\u3053\u306e\u5b9a\u7406\u3092\u767a\u8868\u3057\u307e\u305b\u3093\u3067\u3057\u305f\u304c\u3001\u30b8\u30e7\u30f3 \u30a6\u30a9\u30fc\u30eb\u30ba\u306f\u6700\u7d42\u7684\u306b 1685 \u5e74\u306b\u767a\u8868\u3057\u3001\u3053\u306e\u767a\u898b\u306f\u30cb\u30e5\u30fc\u30c8\u30f3\u306e\u529f\u7e3e\u3067\u3042\u308b\u3068\u8a8d\u3081\u307e\u3057\u305f\u3002<\/p>\n<div id=\"ezoic-pub-ad-placeholder-176\" data-inserter-version=\"-1\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u3053\u306e\u30da\u30fc\u30b8\u3067\u306f\u3001\u30cb\u30e5\u30fc\u30c8\u30f3\u306e\u4e8c\u9805\uff08\u307e\u305f\u306f\u4e8c\u9805\u5b9a\u7406\uff09\u3068\u306f\u4f55\u304b\u3001\u305d\u306e\u516c\u5f0f\u306f\u4f55\u306a\u306e\u304b\u306b\u3064\u3044\u3066\u8aac\u660e\u3057\u307e\u3059\u3002\u30bf\u30eb\u30bf\u30fc\u30ea\u30a2 (\u307e\u305f\u306f\u30d1\u30b9\u30ab\u30eb) \u4e09\u89d2\u5f62\u3092\u4f7f\u7528\u3057\u3066\u3053\u308c\u3092\u7c21\u7565\u5316\u3059\u308b\u65b9\u6cd5\u3082\u308f\u304b\u308a\u307e\u3059\u3002\u3055\u3089\u306b\u3001\u30cb\u30e5\u30fc\u30c8\u30f3\u306e\u4e8c\u9805\u5f0f\u3068\u305d\u306e\u3059\u3079\u3066 &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/ja\/%e4%ba%8c%e9%a0%85%e3%81%be%e3%81%9f%e3%81%af%e3%83%8b%e3%83%a5%e3%83%bc%e3%83%88%e3%83%b3%e3%81%ae%e4%ba%8c%e9%a0%85%e5%ae%9a%e7%90%86%e3%81%ae%e5%85%ac%e5%bc%8f%e3%81%a8%e6%bc%94%e7%bf%92%e5%95%8f\/\"> <span class=\"screen-reader-text\">\u30cb\u30e5\u30fc\u30c8\u30f3\u306e\u4e8c\u9805 (\u4e8c\u9805\u5b9a\u7406)<\/span> \u3082\u3063\u3068\u8aad\u3080 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