{"id":128249,"date":"2017-11-06T09:05:48","date_gmt":"2017-11-06T11:05:48","guid":{"rendered":"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/?p=128249"},"modified":"2026-05-14T19:13:20","modified_gmt":"2026-05-14T21:13:20","slug":"binomio-de-newton","status":"publish","type":"post","link":"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/matematica\/binomio-de-newton","title":{"rendered":"Bin\u00f4mio de Newton"},"content":{"rendered":"<p>O\u00a0<b>Bin\u00f4mio de Newton<\/b> \u00e9 uma f\u00f3rmula matem\u00e1tica utilizada para expandir express\u00f5es da forma <em><strong>(a+b)<sup>n<\/sup><\/strong><\/em>, onde <em><strong>n<\/strong><\/em> \u00e9 um n\u00famero natural. Ele permite calcular pot\u00eancias elevadas, como <strong>(x+2)<sup>7<\/sup><\/strong>, sem realizar distribui\u00e7\u00f5es longas, resultando em uma soma de <strong><em>n+1<\/em><\/strong>\u00a0termos cujos coeficientes s\u00e3o dados por combina\u00e7\u00f5es (n\u00fameros binomiais) ou pelo Tri\u00e2ngulo de Pascal<\/p>\n<p>O\u00a0<b>bin\u00f4mio de Newton<\/b>\u00a0\u00e9 um operador que utiliza fatoriais para o c\u00e1lculo. Essa ferramenta \u00e9\u00a0muito utilizada para o c\u00e1lculo de coeficientes dos termos do tipo (x + y)<sup>n<\/sup>.<\/p>\n<p align=\"center\"><img fetchpriority=\"high\" decoding=\"async\" class=\"aligncenter size-full wp-image-177775\" src=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/11\/binomio-1.jpg\" alt=\"Bin\u00f4mio de Newton\" width=\"237\" height=\"298\" \/><b>Isaac Newton<\/b><\/p>\n<p><strong>O c\u00e1lculo do Bin\u00f4mio de Newton<\/strong><\/p>\n<p>Para calcular o\u00a0<b>Bin\u00f4mio de Newton<\/b>, primeiro precisamos entender o fatorial.\u00a0Um n\u00famero fatorial \u00e9 representado como n! = n (n-1) (n-2) \u2026 (2) (1), ou seja, o produto de\u00a0todos os n\u00fameros de 1 at\u00e9 n.<\/p>\n<p>O\u00a0<b>bin\u00f4mio de Newton\u00a0<\/b>\u00e9 calculado para, n &gt; p e ambos pertencentes ao conjunto dos\u00a0Naturais.<\/p>\n<p align=\"center\"><img decoding=\"async\" class=\"aligncenter size-full wp-image-177776\" src=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/11\/binomio-2.gif\" alt=\"Bin\u00f4mio de Newton\" width=\"198\" height=\"84\" \/><\/p>\n<p align=\"left\"><strong>Exemplo:<\/strong><\/p>\n<p align=\"center\"><img decoding=\"async\" class=\"aligncenter size-full wp-image-177777\" src=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/11\/binomio-3.gif\" alt=\"Bin\u00f4mio de Newton\" width=\"386\" height=\"74\" \/><\/p>\n<p><strong>Algumas propriedades dos Bin\u00f4mios de Newton s\u00e3o:<\/strong><\/p>\n<p><b>Dois bin\u00f4mios de Newton s\u00e3o iguais quando:<\/b><\/p>\n<p align=\"center\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-177778\" src=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/11\/binomio-4.gif\" alt=\"Bin\u00f4mio de Newton\" width=\"274\" height=\"85\" \/><\/p>\n<p align=\"left\"><b>S\u00e3o definidos os seguintes bin\u00f4mios:<\/b><\/p>\n<p align=\"center\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-177779\" src=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/11\/binomio-5.jpg\" alt=\"Bin\u00f4mio de Newton\" width=\"145\" height=\"255\" \/><\/p>\n<p align=\"left\"><strong>A rela\u00e7\u00e3o de Stiffel<\/strong><\/p>\n<p>A rela\u00e7\u00e3o de Stiffel facilita no c\u00e1lculo de soma de bin\u00f4mios de Newton mesmo numerador e\u00a0denominadores consecutivos.<\/p>\n<p align=\"center\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-177780\" src=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/11\/binomio-6.gif\" alt=\"Bin\u00f4mio de Newton\" width=\"330\" height=\"90\" \/><\/p>\n<p><strong>Tri\u00e2ngulo de Pascal<\/strong><\/p>\n<p>O\u00a0<b>tri\u00e2ngulo de Pascal<\/b>\u00a0\u00e9 uma forma de organizar os bin\u00f4mios de Newton a fim de extrair\u00a0resultados r\u00e1pidos atrav\u00e9s das propriedades estabelecidas nas linhas, colunas e\u00a0transversais do tri\u00e2ngulo.<\/p>\n<p align=\"center\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-177781\" src=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/11\/binomio-7.gif\" alt=\"Bin\u00f4mio de Newton\" width=\"356\" height=\"320\" \/><\/p>\n<p><strong>Teorema das Linhas<\/strong><\/p>\n<p>O tri\u00e2ngulo de Pascal tem a soma de cada uma das linhas como pot\u00eancias de 2, isto\u00a0\u00e9, a n-\u00e9sima linha do tri\u00e2ngulo tem a soma igual a 2n.<\/p>\n<p><b>Resolvendo os valores do tri\u00e2ngulo de Pascal temos<\/b>:<\/p>\n<p align=\"center\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-177782\" src=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/11\/binomio-8.gif\" alt=\"Bin\u00f4mio de Newton\" width=\"397\" height=\"294\" \/><\/p>\n<p><strong>Teorema das Colunas<\/strong><\/p>\n<p>A soma de uma coluna no tri\u00e2ngulo de pascal \u00e9 dado pelo n\u00famero binomial da\u00a0diagonal.<\/p>\n<p><b>Vejamos os exemplos:<\/b><\/p>\n<p align=\"center\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-177783\" src=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/11\/binomio-9.jpg\" alt=\"Bin\u00f4mio de Newton\" width=\"399\" height=\"298\" srcset=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/11\/binomio-9.jpg 399w, https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/11\/binomio-9-300x224.jpg 300w\" sizes=\"(max-width: 399px) 100vw, 399px\" \/><\/p>\n<p align=\"left\">Em nossos exemplos, temos as colunas em que\u00a0<strong>1+2+3\u00a0= 6\u00a0<\/strong>e<strong>\u00a01+3=4<\/strong><\/p>\n<p><strong>Teorema das Transversais<\/strong><\/p>\n<p>A soma dos n\u00fameros binomiais de uma transversal \u00e9 igual ao bin\u00f4mio de Newton da\u00a0linha imediatamente abaixo do Tri\u00e2ngulo de Pascal.<\/p>\n<p align=\"center\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-177784\" src=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/11\/binomio-10.jpg\" alt=\"Bin\u00f4mio de Newton\" width=\"396\" height=\"297\" srcset=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/11\/binomio-10.jpg 396w, https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/11\/binomio-10-300x225.jpg 300w\" sizes=\"(max-width: 396px) 100vw, 396px\" \/><\/p>\n<p><strong>Fonte:<\/strong>\u00a0Col\u00e9gio S\u00e3o Francisco\/Luisa Boccardo Burini<\/p>\n","protected":false},"excerpt":{"rendered":"<p>O\u00a0Bin\u00f4mio de Newton \u00e9 uma f\u00f3rmula matem\u00e1tica utilizada para expandir express\u00f5es da forma (a+b)n, onde n \u00e9 um n\u00famero natural. Ele permite calcular pot\u00eancias elevadas, como (x+2)7, sem realizar distribui\u00e7\u00f5es longas, resultando em uma soma de n+1\u00a0termos cujos coeficientes s\u00e3o dados por combina\u00e7\u00f5es (n\u00fameros binomiais) ou pelo Tri\u00e2ngulo de Pascal O\u00a0bin\u00f4mio de Newton\u00a0\u00e9 um operador [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":128263,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[414],"tags":[],"class_list":["post-128249","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-matematica"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v28.5 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Bin\u00f4mio de Newton, Teorema Bin\u00f4mio de Newton<\/title>\n<meta name=\"description\" content=\"Bin\u00f4mio de Newton, Teorema, Bin\u00f4mio, Tri\u00e2ngulo, Matem\u00e1tica, F\u00f3rmula, C\u00e1lculo, Propriedades, Exemplo, Bin\u00f4mio de Newton\" \/>\n<meta name=\"robots\" content=\"noindex, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<meta property=\"og:locale\" content=\"pt_BR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Bin\u00f4mio de Newton, Teorema Bin\u00f4mio de Newton\" \/>\n<meta property=\"og:description\" content=\"Bin\u00f4mio de Newton, Teorema, Bin\u00f4mio, Tri\u00e2ngulo, Matem\u00e1tica, F\u00f3rmula, C\u00e1lculo, Propriedades, Exemplo, Bin\u00f4mio de Newton\" \/>\n<meta property=\"og:url\" content=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/matematica\/binomio-de-newton\" \/>\n<meta property=\"og:site_name\" content=\"Portal S\u00e3o Francisco\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/Portal-S%c3%a3o-Francisco-230719150302226\/\" \/>\n<meta property=\"article:published_time\" content=\"2017-11-06T11:05:48+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2026-05-14T21:13:20+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/11\/binomio-de-newton.jpg\" \/>\n\t<meta property=\"og:image:width\" content=\"400\" \/>\n\t<meta property=\"og:image:height\" content=\"300\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/jpeg\" \/>\n<meta name=\"author\" content=\"Augusto Abreu\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Escrito por\" \/>\n\t<meta name=\"twitter:data1\" content=\"Augusto Abreu\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. tempo de leitura\" \/>\n\t<meta name=\"twitter:data2\" content=\"4 minutos\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\\\/\\\/lab.fabricadelandings.com.br\\\/portalsaofrancisconovo\\\/matematica\\\/binomio-de-newton#article\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/lab.fabricadelandings.com.br\\\/portalsaofrancisconovo\\\/matematica\\\/binomio-de-newton\"},\"author\":{\"name\":\"Augusto Abreu\",\"@id\":\"https:\\\/\\\/lab.fabricadelandings.com.br\\\/portalsaofrancisconovo\\\/#\\\/schema\\\/person\\\/7bbc8022c9c2c63e2e4afadfde4db578\"},\"headline\":\"Bin\u00f4mio de Newton\",\"datePublished\":\"2017-11-06T11:05:48+00:00\",\"dateModified\":\"2026-05-14T21:13:20+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\\\/\\\/lab.fabricadelandings.com.br\\\/portalsaofrancisconovo\\\/matematica\\\/binomio-de-newton\"},\"wordCount\":360,\"commentCount\":0,\"image\":{\"@id\":\"https:\\\/\\\/lab.fabricadelandings.com.br\\\/portalsaofrancisconovo\\\/matematica\\\/binomio-de-newton#primaryimage\"},\"thumbnailUrl\":\"https:\\\/\\\/lab.fabricadelandings.com.br\\\/portalsaofrancisconovo\\\/wp-content\\\/uploads\\\/2017\\\/11\\\/binomio-de-newton.jpg\",\"articleSection\":[\"Matem\u00e1tica\"],\"inLanguage\":\"pt-BR\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\\\/\\\/lab.fabricadelandings.com.br\\\/portalsaofrancisconovo\\\/matematica\\\/binomio-de-newton#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/lab.fabricadelandings.com.br\\\/portalsaofrancisconovo\\\/matematica\\\/binomio-de-newton\",\"url\":\"https:\\\/\\\/lab.fabricadelandings.com.br\\\/portalsaofrancisconovo\\\/matematica\\\/binomio-de-newton\",\"name\":\"Bin\u00f4mio de Newton, Teorema Bin\u00f4mio de Newton\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/lab.fabricadelandings.com.br\\\/portalsaofrancisconovo\\\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\\\/\\\/lab.fabricadelandings.com.br\\\/portalsaofrancisconovo\\\/matematica\\\/binomio-de-newton#primaryimage\"},\"image\":{\"@id\":\"https:\\\/\\\/lab.fabricadelandings.com.br\\\/portalsaofrancisconovo\\\/matematica\\\/binomio-de-newton#primaryimage\"},\"thumbnailUrl\":\"https:\\\/\\\/lab.fabricadelandings.com.br\\\/portalsaofrancisconovo\\\/wp-content\\\/uploads\\\/2017\\\/11\\\/binomio-de-newton.jpg\",\"datePublished\":\"2017-11-06T11:05:48+00:00\",\"dateModified\":\"2026-05-14T21:13:20+00:00\",\"author\":{\"@id\":\"https:\\\/\\\/lab.fabricadelandings.com.br\\\/portalsaofrancisconovo\\\/#\\\/schema\\\/person\\\/7bbc8022c9c2c63e2e4afadfde4db578\"},\"description\":\"Bin\u00f4mio de Newton, Teorema, Bin\u00f4mio, Tri\u00e2ngulo, Matem\u00e1tica, F\u00f3rmula, C\u00e1lculo, Propriedades, Exemplo, Bin\u00f4mio de Newton\",\"breadcrumb\":{\"@id\":\"https:\\\/\\\/lab.fabricadelandings.com.br\\\/portalsaofrancisconovo\\\/matematica\\\/binomio-de-newton#breadcrumb\"},\"inLanguage\":\"pt-BR\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\\\/\\\/lab.fabricadelandings.com.br\\\/portalsaofrancisconovo\\\/matematica\\\/binomio-de-newton\"]}]},{\"@type\":\"ImageObject\",\"inLanguage\":\"pt-BR\",\"@id\":\"https:\\\/\\\/lab.fabricadelandings.com.br\\\/portalsaofrancisconovo\\\/matematica\\\/binomio-de-newton#primaryimage\",\"url\":\"https:\\\/\\\/lab.fabricadelandings.com.br\\\/portalsaofrancisconovo\\\/wp-content\\\/uploads\\\/2017\\\/11\\\/binomio-de-newton.jpg\",\"contentUrl\":\"https:\\\/\\\/lab.fabricadelandings.com.br\\\/portalsaofrancisconovo\\\/wp-content\\\/uploads\\\/2017\\\/11\\\/binomio-de-newton.jpg\",\"width\":400,\"height\":300,\"caption\":\"Bin\u00f4mio de Newton\"},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\\\/\\\/lab.fabricadelandings.com.br\\\/portalsaofrancisconovo\\\/matematica\\\/binomio-de-newton#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"In\u00edcio\",\"item\":\"https:\\\/\\\/lab.fabricadelandings.com.br\\\/portalsaofrancisconovo\\\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Matem\u00e1tica\",\"item\":\"https:\\\/\\\/lab.fabricadelandings.com.br\\\/portalsaofrancisconovo\\\/categoria\\\/matematica\"},{\"@type\":\"ListItem\",\"position\":3,\"name\":\"Bin\u00f4mio de Newton\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\\\/\\\/lab.fabricadelandings.com.br\\\/portalsaofrancisconovo\\\/#website\",\"url\":\"https:\\\/\\\/lab.fabricadelandings.com.br\\\/portalsaofrancisconovo\\\/\",\"name\":\"Portal S\u00e3o Francisco\",\"description\":\"Pesquisa Escolar Gratuita\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\\\/\\\/lab.fabricadelandings.com.br\\\/portalsaofrancisconovo\\\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"pt-BR\"},{\"@type\":\"Person\",\"@id\":\"https:\\\/\\\/lab.fabricadelandings.com.br\\\/portalsaofrancisconovo\\\/#\\\/schema\\\/person\\\/7bbc8022c9c2c63e2e4afadfde4db578\",\"name\":\"Augusto Abreu\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Bin\u00f4mio de Newton, Teorema Bin\u00f4mio de Newton","description":"Bin\u00f4mio de Newton, Teorema, Bin\u00f4mio, Tri\u00e2ngulo, Matem\u00e1tica, F\u00f3rmula, C\u00e1lculo, Propriedades, Exemplo, Bin\u00f4mio de Newton","robots":{"index":"noindex","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"og_locale":"pt_BR","og_type":"article","og_title":"Bin\u00f4mio de Newton, Teorema Bin\u00f4mio de Newton","og_description":"Bin\u00f4mio de Newton, Teorema, Bin\u00f4mio, Tri\u00e2ngulo, Matem\u00e1tica, F\u00f3rmula, C\u00e1lculo, Propriedades, Exemplo, Bin\u00f4mio de Newton","og_url":"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/matematica\/binomio-de-newton","og_site_name":"Portal S\u00e3o Francisco","article_publisher":"https:\/\/www.facebook.com\/Portal-S%c3%a3o-Francisco-230719150302226\/","article_published_time":"2017-11-06T11:05:48+00:00","article_modified_time":"2026-05-14T21:13:20+00:00","og_image":[{"width":400,"height":300,"url":"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/11\/binomio-de-newton.jpg","type":"image\/jpeg"}],"author":"Augusto Abreu","twitter_card":"summary_large_image","twitter_misc":{"Escrito por":"Augusto Abreu","Est. tempo de leitura":"4 minutos"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/matematica\/binomio-de-newton#article","isPartOf":{"@id":"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/matematica\/binomio-de-newton"},"author":{"name":"Augusto Abreu","@id":"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/#\/schema\/person\/7bbc8022c9c2c63e2e4afadfde4db578"},"headline":"Bin\u00f4mio de Newton","datePublished":"2017-11-06T11:05:48+00:00","dateModified":"2026-05-14T21:13:20+00:00","mainEntityOfPage":{"@id":"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/matematica\/binomio-de-newton"},"wordCount":360,"commentCount":0,"image":{"@id":"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/matematica\/binomio-de-newton#primaryimage"},"thumbnailUrl":"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/11\/binomio-de-newton.jpg","articleSection":["Matem\u00e1tica"],"inLanguage":"pt-BR","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/matematica\/binomio-de-newton#respond"]}]},{"@type":"WebPage","@id":"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/matematica\/binomio-de-newton","url":"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/matematica\/binomio-de-newton","name":"Bin\u00f4mio de Newton, Teorema Bin\u00f4mio de Newton","isPartOf":{"@id":"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/#website"},"primaryImageOfPage":{"@id":"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/matematica\/binomio-de-newton#primaryimage"},"image":{"@id":"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/matematica\/binomio-de-newton#primaryimage"},"thumbnailUrl":"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/11\/binomio-de-newton.jpg","datePublished":"2017-11-06T11:05:48+00:00","dateModified":"2026-05-14T21:13:20+00:00","author":{"@id":"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/#\/schema\/person\/7bbc8022c9c2c63e2e4afadfde4db578"},"description":"Bin\u00f4mio de Newton, Teorema, Bin\u00f4mio, Tri\u00e2ngulo, Matem\u00e1tica, F\u00f3rmula, C\u00e1lculo, Propriedades, Exemplo, Bin\u00f4mio de Newton","breadcrumb":{"@id":"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/matematica\/binomio-de-newton#breadcrumb"},"inLanguage":"pt-BR","potentialAction":[{"@type":"ReadAction","target":["https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/matematica\/binomio-de-newton"]}]},{"@type":"ImageObject","inLanguage":"pt-BR","@id":"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/matematica\/binomio-de-newton#primaryimage","url":"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/11\/binomio-de-newton.jpg","contentUrl":"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/11\/binomio-de-newton.jpg","width":400,"height":300,"caption":"Bin\u00f4mio de Newton"},{"@type":"BreadcrumbList","@id":"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/matematica\/binomio-de-newton#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"In\u00edcio","item":"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/"},{"@type":"ListItem","position":2,"name":"Matem\u00e1tica","item":"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/categoria\/matematica"},{"@type":"ListItem","position":3,"name":"Bin\u00f4mio de Newton"}]},{"@type":"WebSite","@id":"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/#website","url":"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/","name":"Portal S\u00e3o Francisco","description":"Pesquisa Escolar Gratuita","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"pt-BR"},{"@type":"Person","@id":"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/#\/schema\/person\/7bbc8022c9c2c63e2e4afadfde4db578","name":"Augusto Abreu"}]}},"_links":{"self":[{"href":"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-json\/wp\/v2\/posts\/128249","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-json\/wp\/v2\/comments?post=128249"}],"version-history":[{"count":2,"href":"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-json\/wp\/v2\/posts\/128249\/revisions"}],"predecessor-version":[{"id":177785,"href":"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-json\/wp\/v2\/posts\/128249\/revisions\/177785"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-json\/wp\/v2\/media\/128263"}],"wp:attachment":[{"href":"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-json\/wp\/v2\/media?parent=128249"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-json\/wp\/v2\/categories?post=128249"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-json\/wp\/v2\/tags?post=128249"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}