{"id":262239,"date":"2025-07-20T13:23:30","date_gmt":"2025-07-20T13:23:30","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=262239"},"modified":"2025-07-20T13:23:32","modified_gmt":"2025-07-20T13:23:32","slug":"express-x-62-as-a-trinomial-in-standard-form-2","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/20\/express-x-62-as-a-trinomial-in-standard-form-2\/","title":{"rendered":"Express (x + 6)2 as a trinomial in standard form."},"content":{"rendered":"\n<p>Express (x + 6)2 as a trinomial in standard form.<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To express (x+6)2(x + 6)^2(x+6)2 as a trinomial in standard form, we start by applying the formula for the square of a binomial:(a+b)2=a2+2ab+b2(a + b)^2 = a^2 + 2ab + b^2(a+b)2=a2+2ab+b2<\/p>\n\n\n\n<p>Here, a=xa = xa=x and b=6b = 6b=6. Now, substitute these values into the formula:(x+6)2=x2+2(x)(6)+62(x + 6)^2 = x^2 + 2(x)(6) + 6^2(x+6)2=x2+2(x)(6)+62<\/p>\n\n\n\n<p>First, simplify each term:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>x2x^2&#215;2 remains as is.<\/li>\n\n\n\n<li>2(x)(6)=12&#215;2(x)(6) = 12&#215;2(x)(6)=12x.<\/li>\n\n\n\n<li>62=366^2 = 3662=36.<\/li>\n<\/ul>\n\n\n\n<p>Now, put everything together:(x+6)2=x2+12x+36(x + 6)^2 = x^2 + 12x + 36(x+6)2=x2+12x+36<\/p>\n\n\n\n<p>So, the trinomial in standard form is:x2+12x+36x^2 + 12x + 36&#215;2+12x+36<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<p>The expression (x+6)2(x + 6)^2(x+6)2 represents a binomial squared, meaning it is the product of the binomial (x+6)(x + 6)(x+6) with itself. To simplify this, we use the square of a binomial formula. This formula breaks the squaring process into three parts:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Square the first term<\/strong>: The square of xxx is x2x^2&#215;2.<\/li>\n\n\n\n<li><strong>Multiply the two terms and double it<\/strong>: Multiply xxx and 666, which gives 6x6x6x, and then double it to get 12x12x12x.<\/li>\n\n\n\n<li><strong>Square the second term<\/strong>: The square of 666 is 363636.<\/li>\n<\/ol>\n\n\n\n<p>After simplifying all terms, we obtain the trinomial x2+12x+36x^2 + 12x + 36&#215;2+12x+36. This is the expanded form of the binomial expression (x+6)2(x + 6)^2(x+6)2, and it is written in standard form because it is in the form of a polynomial with terms in descending powers of xxx.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner6-1222.jpeg\" alt=\"\" class=\"wp-image-262242\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Express (x + 6)2 as a trinomial in standard form. The Correct Answer and Explanation is: To express (x+6)2(x + 6)^2(x+6)2 as a trinomial in standard form, we start by applying the formula for the square of a binomial:(a+b)2=a2+2ab+b2(a + b)^2 = a^2 + 2ab + b^2(a+b)2=a2+2ab+b2 Here, a=xa = xa=x and b=6b = 6b=6. [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","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":"","ast-disable-related-posts":"","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":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-262239","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/262239","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=262239"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/262239\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=262239"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=262239"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=262239"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}