{"id":348,"date":"2023-07-06T01:29:47","date_gmt":"2023-07-06T01:29:47","guid":{"rendered":"https:\/\/mathority.org\/pt\/binomios\/"},"modified":"2023-07-06T01:29:47","modified_gmt":"2023-07-06T01:29:47","slug":"binomios","status":"publish","type":"post","link":"https:\/\/mathority.org\/pt\/binomios\/","title":{"rendered":"Bin\u00f4mios"},"content":{"rendered":"<p>Nesta p\u00e1gina voc\u00ea encontrar\u00e1 uma explica\u00e7\u00e3o do que \u00e9 um bin\u00f4mio e, al\u00e9m disso, poder\u00e1 ver exemplos de cada tipo de bin\u00f4mio. Al\u00e9m disso, mostramos as f\u00f3rmulas usadas para resolver opera\u00e7\u00f5es com bin\u00f4mios: multiplica\u00e7\u00e3o de bin\u00f4mios, bin\u00f4mio ao quadrado, bin\u00f4mio ao cubo,\u2026<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%C2%BFQue-es-un-binomio\"><\/span> O que \u00e9 um par?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Em \u00e1lgebra, a defini\u00e7\u00e3o de um bin\u00f4mio \u00e9:<\/p>\n<p> <strong>Um bin\u00f4mio \u00e9 um polin\u00f4mio composto por apenas dois mon\u00f4mios<\/strong> . Em outras palavras, um bin\u00f4mio consiste em uma express\u00e3o alg\u00e9brica com apenas 2 termos diferentes unidos pelo sinal de mais (+) ou pelo sinal de menos (-). <\/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.png\" alt=\"o que s\u00e3o bin\u00f4mios\" class=\"wp-image-2992\" width=\"159\" height=\"159\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> A palavra binomial vem do grego e \u00e9 composta por dois componentes lexicais ( <em>bi<\/em> e <em>nomos<\/em> ), que significam o seguinte:<\/p>\n<ul>\n<li> <em>bi<\/em> : prefixo que significa 2.<\/li>\n<li> <em>nomos<\/em> : significa parte.<\/li>\n<\/ul>\n<p> Podemos, portanto, deduzir o significado do bin\u00f4mio: polin\u00f4mio com duas partes (ou 2 mon\u00f4mios).<\/p>\n<p> Por outro lado, o conceito de par tem outro significado que n\u00e3o o matem\u00e1tico, nomeadamente que um par tamb\u00e9m pode designar um conjunto de duas personalidades que t\u00eam um papel protagonista na vida pol\u00edtica, em determinadas modalidades desportivas ou mesmo no entretenimento. . Mas, obviamente, focaremos aqui na defini\u00e7\u00e3o matem\u00e1tica do bin\u00f4mio.<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Ejemplos-de-binomios\"><\/span> Exemplos de bin\u00f4mios<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Para finalizar a compreens\u00e3o da no\u00e7\u00e3o de bin\u00f4mio, veremos v\u00e1rios exemplos desse tipo de polin\u00f4mio:<\/p>\n<ul>\n<li> Exemplo de um bin\u00f4mio quadr\u00e1tico:<\/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-05fba89f2955eb2762904c8527e26aa8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^2+4x\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"58\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<ul>\n<li> Exemplo de bin\u00f4mio de terceiro grau:<\/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-ae722155bf9498cffea4c08b7015fbee_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^3+5\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"47\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<ul>\n<li> Exemplo de bin\u00f4mio de quarto grau:<\/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-0e6e322cb58245ab80d095c0a81fc631_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"3x^4+8x^2\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"74\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p> Agora que sabemos o que \u00e9 um bin\u00f4mio, veremos os diferentes tipos de bin\u00f4mios que existem e como as opera\u00e7\u00f5es com bin\u00f4mios s\u00e3o resolvidas.<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Binomio-al-cuadrado\"><\/span> bin\u00f4mio ao quadrado<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Um <strong>bin\u00f4mio quadrado<\/strong> \u00e9 uma identidade not\u00e1vel, tamb\u00e9m chamada de produto not\u00e1vel ou igualdade not\u00e1vel. Resolver a pot\u00eancia de um bin\u00f4mio elevado a 2 depende se \u00e9 um bin\u00f4mio de soma ou um bin\u00f4mio de diferen\u00e7a.<\/p>\n<p> Uma soma binomial refere-se \u00e0quele bin\u00f4mio cujos dois termos s\u00e3o positivos, ou seja, uma soma binomial quadrada \u00e9:<\/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-ef98ef741811c17cd99e75e5f848ea69_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a+b)^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"59\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Por outro lado, um bin\u00f4mio de diferen\u00e7a (ou subtra\u00e7\u00e3o) \u00e9 o conjugado do bin\u00f4mio de adi\u00e7\u00e3o, ou seja, um de seus mon\u00f4mios tem sinal negativo. Portanto, a express\u00e3o alg\u00e9brica para uma diferen\u00e7a binomial quadrada \u00e9:<\/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-8f88949b2f3fcc20e9d00f495e471cf2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a-b)^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"59\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Para calcular um bin\u00f4mio quadrado, \u00e9 necess\u00e1rio aplicar uma f\u00f3rmula que, como vimos, varia dependendo se se trata de uma adi\u00e7\u00e3o ou subtra\u00e7\u00e3o. Descubra como isso \u00e9 feito nas <a href=\"https:\/\/mathority.org\/pt\/identidades-produtos-igualdades-notaveis-exercicios-resolvidos\/\"><strong><span style=\"text-decoration: underline;\">f\u00f3rmulas de igualdades not\u00e1veis<\/span><\/strong><\/a> , onde voc\u00ea pode ver todas as explica\u00e7\u00f5es passo a passo, bem como exemplos e exerc\u00edcios resolvidos, e n\u00e3o apenas dessas 2 igualdades not\u00e1veis, mas de todas elas.<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Binomio-al-cubo\"><\/span> bin\u00f4mio ao cubo<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Embora usados com menos frequ\u00eancia, <strong>os bin\u00f4mios c\u00fabicos<\/strong> tamb\u00e9m s\u00e3o considerados produtos not\u00e1veis. Ou em outras palavras, existem regras matem\u00e1ticas que permitem encontrar rapidamente o cubo de um bin\u00f4mio (voc\u00ea pode v\u00ea-las no link acima <em><span style=\"text-decoration: underline;\">de f\u00f3rmulas de identidades not\u00e1veis<\/span><\/em> ).<\/p>\n<p> Como antes, o resultado desta potencia\u00e7\u00e3o depende se \u00e9 o cubo de uma soma:<\/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-380239d5f1b18e11f3b6b0931a4f14d9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a+b)^3\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"59\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Ou se, pelo contr\u00e1rio, a pot\u00eancia \u00e9 constitu\u00edda pelo cubo de uma diferen\u00e7a ou de uma subtra\u00e7\u00e3o:<\/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-6a48c875098bfee5d50068c1f0e7296d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a-b)^3\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"59\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Logicamente, a principal diferen\u00e7a entre um bin\u00f4mio quadrado e um bin\u00f4mio c\u00fabico \u00e9 o expoente de pot\u00eancia. No entanto, a f\u00f3rmula para um bin\u00f4mio ao cubo \u00e9 muito mais complicada do que a de um bin\u00f4mio ao quadrado.<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Binomios-notables\"><\/span> acordos not\u00e1veis<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Existem, em particular, certos tipos de bin\u00f4mios que s\u00e3o um pouco particulares pelas suas caracter\u00edsticas, pois correspondem a identidades not\u00e1veis (ou produtos not\u00e1veis) menos conhecidas.<\/p>\n<ul>\n<li> Soma dos quadrados:\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4609cf46d75484e45152fba69537c2ce_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a^2+b^2\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"54\" style=\"vertical-align: -2px;\"><\/p>\n<\/li>\n<li> Diferen\u00e7a (ou subtra\u00e7\u00e3o) de quadrados:\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3e8c1ff5ed178c14d02192ff8c85b93b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a^2-b^2\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"54\" style=\"vertical-align: 0px;\"><\/p>\n<\/li>\n<li> Soma dos cubos:\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-945df8cc421a5647ed318b39d5e031f8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a^3+b^3\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"54\" style=\"vertical-align: -2px;\"><\/p>\n<\/li>\n<li> Diferen\u00e7a (ou subtra\u00e7\u00e3o) de cubos:\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-932403564d7ffe6622096bd031b4fd28_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a^3-b^3\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"54\" style=\"vertical-align: 0px;\"><\/p>\n<\/li>\n<\/ul>\n<p> Ouro<\/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-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> E<\/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> s\u00e3o quaisquer dois mon\u00f4mios.<\/p>\n<p> Embora essas express\u00f5es binomiais se pare\u00e7am muito com as que vimos acima (binomial ao quadrado e binomial ao cubo), se voc\u00ea olhar com aten\u00e7\u00e3o elas s\u00e3o diferentes. Nesse sentido, voc\u00ea tamb\u00e9m pode ver as f\u00f3rmulas dos bin\u00f4mios not\u00e1veis e suas dedu\u00e7\u00f5es clicando no link acima \u2b06 <em><span style=\"text-decoration: underline;\">f\u00f3rmulas das identidades not\u00e1veis.\u2b06<\/span><\/em> <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Multiplicacion-de-binomios\"><\/span> multiplica\u00e7\u00e3o binomial<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Uma das opera\u00e7\u00f5es mais comuns com bin\u00f4mios \u00e9 a multiplica\u00e7\u00e3o. A seguir veremos um exemplo de como calcular uma multiplica\u00e7\u00e3o entre bin\u00f4mios.<\/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-47234e6d6426b9822cf5b535eeb2d93f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x^2+2x)\\cdot (x-5)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"138\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Para calcular a multiplica\u00e7\u00e3o binomial, devemos primeiro multiplicar cada termo do primeiro bin\u00f4mio por cada termo do segundo bin\u00f4mio:<\/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-35c53275367a4876b719354ba10220a2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^2\\cdot x+x^2\\cdot (-5)+2x\\cdot x +2x\\cdot (-5)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"283\" 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-8bac17566196aeb84f84fcabbec84ed0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^3-5x^2+2x^2 -10x\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"164\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p> A seguir, agrupamos termos semelhantes, ou seja, possuem a mesma parte literal:<\/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-6b1a70c63520e6d05a13d725480c7ba3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{x^3-3x^2 -10x}\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"116\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> E assim conseguimos encontrar o resultado do produto entre os pares. <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Producto-de-dos-binomios-con-un-termino-comun\"><\/span> Produto de dois bin\u00f4mios com um termo comum<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> Quando os bin\u00f4mios que participam da multiplica\u00e7\u00e3o t\u00eam como termo comum a vari\u00e1vel<\/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-038741496726a75b03e91a2e030b0287_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x,\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: -4px;\"><\/p>\n<p> Existe uma f\u00f3rmula para calcular rapidamente esta opera\u00e7\u00e3o binomial:<\/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-0d402b74334bc5f53aec7f1ed85a2f5b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x+a)(x+b) = x^2+(a+b)x+ab\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"272\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Aqui mostramos um exerc\u00edcio resolvido para que voc\u00ea veja como aplicar esta f\u00f3rmula: <\/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-8447db6a2246c09b2e7be29f8050a3d6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned} (x+4)(x+5) &amp;= x^2+(4+5)x+4\\cdot 5 \\\\[2ex] &amp; = x^2+9x+20 \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"62\" width=\"286\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Binomio-de-Newton\"><\/span> Bin\u00f4mio de Newton<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>O bin\u00f4mio de Newton<\/strong> , tamb\u00e9m chamado <strong>de teorema binomial,<\/strong> \u00e9 uma f\u00f3rmula usada para calcular as pot\u00eancias dos bin\u00f4mios. <\/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\"> A <strong>f\u00f3rmula matem\u00e1tica para o bin\u00f4mio de Newton<\/strong> \u00e9 a seguinte:<\/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-73be038011b09c44860e6a3aac0ddeee_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}x^{n-k}y^k\" title=\"Rendered by QuickLaTeX.com\" height=\"50\" width=\"206\" style=\"vertical-align: -22px;\"><\/p>\n<\/p>\n<p> Ou equivalente:<\/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> Como voc\u00ea pode ver, esta f\u00f3rmula \u00e9 um pouco complexa de entender. \u00c9 por isso que fizemos abaixo as pot\u00eancias dos bin\u00f4mios de menor grau para que voc\u00ea possa entender melhor: <\/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=\"f\u00f3rmula para o teorema binomial de newton\" class=\"wp-image-2126\" width=\"578\" height=\"578\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> Esta f\u00f3rmula pode ser um pouco entediante para calcular bin\u00f4mios quadrados ou c\u00fabicos, pois, como vimos acima, existem f\u00f3rmulas mais simples. Por\u00e9m, o bin\u00f4mio de Newton \u00e9 muito \u00fatil para encontrar pot\u00eancias de grau superior, por exemplo, \u00e9 amplamente utilizado para determinar um bin\u00f4mio elevado \u00e0 quarta.<\/p>\n<p> Mas para aplicar esta f\u00f3rmula \u00e9 necess\u00e1rio saber calcular um n\u00famero combinat\u00f3rio, ou seja, a express\u00e3o alg\u00e9brica do tipo<\/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> , c\u00e1lculo n\u00e3o \u00e9 f\u00e1cil. \ud83d\udd0d <span style=\"text-decoration: underline;\">\u00c9 por isso que recomendamos que voc\u00ea pesquise como isso \u00e9 feito em nosso mecanismo de busca no canto superior direito<\/span> \ud83d\udd0e, voc\u00ea encontrar\u00e1 nosso artigo onde explicamos esta opera\u00e7\u00e3o passo a passo.<\/p>\n<div id=\"ezoic-pub-ad-placeholder-176\" data-inserter-version=\"-1\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Nesta p\u00e1gina voc\u00ea encontrar\u00e1 uma explica\u00e7\u00e3o do que \u00e9 um bin\u00f4mio e, al\u00e9m disso, poder\u00e1 ver exemplos de cada tipo de bin\u00f4mio. Al\u00e9m disso, mostramos as f\u00f3rmulas usadas para resolver opera\u00e7\u00f5es com bin\u00f4mios: multiplica\u00e7\u00e3o de bin\u00f4mios, bin\u00f4mio ao quadrado, bin\u00f4mio ao cubo,\u2026 O que \u00e9 um par? Em \u00e1lgebra, a defini\u00e7\u00e3o de um bin\u00f4mio \u00e9: &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/pt\/binomios\/\"> <span class=\"screen-reader-text\">Bin\u00f4mios<\/span> Leia mais &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"","footnotes":""},"categories":[7],"tags":[],"class_list":["post-348","post","type-post","status-publish","format-standard","hentry","category-binomios"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.2 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Bin\u00f4mios - Matoridade<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathority.org\/pt\/binomios\/\" \/>\n<meta property=\"og:locale\" content=\"pt_BR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Bin\u00f4mios - Matoridade\" \/>\n<meta property=\"og:description\" content=\"Nesta p\u00e1gina voc\u00ea encontrar\u00e1 uma explica\u00e7\u00e3o do que \u00e9 um bin\u00f4mio e, al\u00e9m disso, poder\u00e1 ver exemplos de cada tipo de bin\u00f4mio. Al\u00e9m disso, mostramos as f\u00f3rmulas usadas para resolver opera\u00e7\u00f5es com bin\u00f4mios: multiplica\u00e7\u00e3o de bin\u00f4mios, bin\u00f4mio ao quadrado, bin\u00f4mio ao cubo,\u2026 O que \u00e9 um par? Em \u00e1lgebra, a defini\u00e7\u00e3o de um bin\u00f4mio \u00e9: &hellip; Bin\u00f4mios Leia mais &raquo;\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathority.org\/pt\/binomios\/\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-06T01:29:47+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/binome.png\" \/>\n<meta name=\"author\" content=\"Equipe Mathoridade\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Escrito por\" \/>\n\t<meta name=\"twitter:data1\" content=\"Equipe Mathoridade\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. tempo de leitura\" \/>\n\t<meta name=\"twitter:data2\" content=\"5 minutos\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/mathority.org\/pt\/binomios\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/mathority.org\/pt\/binomios\/\"},\"author\":{\"name\":\"Equipe Mathoridade\",\"@id\":\"https:\/\/mathority.org\/pt\/#\/schema\/person\/26defeb7b79f5baaedafa33a1ac6ac00\"},\"headline\":\"Bin\u00f4mios\",\"datePublished\":\"2023-07-06T01:29:47+00:00\",\"dateModified\":\"2023-07-06T01:29:47+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/mathority.org\/pt\/binomios\/\"},\"wordCount\":1027,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/mathority.org\/pt\/#organization\"},\"articleSection\":[\"Bin\u00f4mios\"],\"inLanguage\":\"pt-BR\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/mathority.org\/pt\/binomios\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/mathority.org\/pt\/binomios\/\",\"url\":\"https:\/\/mathority.org\/pt\/binomios\/\",\"name\":\"Bin\u00f4mios - Matoridade\",\"isPartOf\":{\"@id\":\"https:\/\/mathority.org\/pt\/#website\"},\"datePublished\":\"2023-07-06T01:29:47+00:00\",\"dateModified\":\"2023-07-06T01:29:47+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/mathority.org\/pt\/binomios\/#breadcrumb\"},\"inLanguage\":\"pt-BR\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/mathority.org\/pt\/binomios\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/mathority.org\/pt\/binomios\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/mathority.org\/pt\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Bin\u00f4mios\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/mathority.org\/pt\/#website\",\"url\":\"https:\/\/mathority.org\/pt\/\",\"name\":\"Mathority\",\"description\":\"Onde a curiosidade encontra o c\u00e1lculo!\",\"publisher\":{\"@id\":\"https:\/\/mathority.org\/pt\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/mathority.org\/pt\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"pt-BR\"},{\"@type\":\"Organization\",\"@id\":\"https:\/\/mathority.org\/pt\/#organization\",\"name\":\"Mathority\",\"url\":\"https:\/\/mathority.org\/pt\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"pt-BR\",\"@id\":\"https:\/\/mathority.org\/pt\/#\/schema\/logo\/image\/\",\"url\":\"https:\/\/mathority.org\/pt\/wp-content\/uploads\/2023\/10\/mathority-logo.png\",\"contentUrl\":\"https:\/\/mathority.org\/pt\/wp-content\/uploads\/2023\/10\/mathority-logo.png\",\"width\":703,\"height\":151,\"caption\":\"Mathority\"},\"image\":{\"@id\":\"https:\/\/mathority.org\/pt\/#\/schema\/logo\/image\/\"}},{\"@type\":\"Person\",\"@id\":\"https:\/\/mathority.org\/pt\/#\/schema\/person\/26defeb7b79f5baaedafa33a1ac6ac00\",\"name\":\"Equipe Mathoridade\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"pt-BR\",\"@id\":\"https:\/\/mathority.org\/pt\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/8a35e4c8616d1c34c03ca02862b580f4372c5650665668489db53a09579bbc4f?s=96&d=mm&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/8a35e4c8616d1c34c03ca02862b580f4372c5650665668489db53a09579bbc4f?s=96&d=mm&r=g\",\"caption\":\"Equipe Mathoridade\"},\"sameAs\":[\"http:\/\/mathority.org\/pt\"]}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Bin\u00f4mios - Matoridade","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/mathority.org\/pt\/binomios\/","og_locale":"pt_BR","og_type":"article","og_title":"Bin\u00f4mios - Matoridade","og_description":"Nesta p\u00e1gina voc\u00ea encontrar\u00e1 uma explica\u00e7\u00e3o do que \u00e9 um bin\u00f4mio e, al\u00e9m disso, poder\u00e1 ver exemplos de cada tipo de bin\u00f4mio. 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