{"id":152744,"date":"2024-10-11T20:35:06","date_gmt":"2024-10-11T20:35:06","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=152744"},"modified":"2024-10-11T20:35:10","modified_gmt":"2024-10-11T20:35:10","slug":"which-expression-is-equivalent-to-the-given-expression","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/10\/11\/which-expression-is-equivalent-to-the-given-expression\/","title":{"rendered":"Which expression is equivalent to the given expression"},"content":{"rendered":"\n<p>Which expression is equivalent to the given expression ? (3y-4) (2y+7) +11y-9  <\/p>\n\n\n\n<p>A. 16y-6 <\/p>\n\n\n\n<p>B. 6y+11y +19 <\/p>\n\n\n\n<p>C. 6y +24y-37 <\/p>\n\n\n\n<p>D. 9y-37<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To find which expression is equivalent to ((3y &#8211; 4)(2y + 7) + 11y &#8211; 9), we need to first expand the expression ((3y &#8211; 4)(2y + 7)) and then combine like terms with the additional terms (11y) and (-9).<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Expand ((3y &#8211; 4)(2y + 7))<\/h3>\n\n\n\n<p>Using the distributive property (also known as the FOIL method for binomials), we can expand:<\/p>\n\n\n\n<p>[<br>(3y &#8211; 4)(2y + 7) = 3y \\cdot 2y + 3y \\cdot 7 &#8211; 4 \\cdot 2y &#8211; 4 \\cdot 7<br>]<\/p>\n\n\n\n<p>Calculating each term:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>(3y \\cdot 2y = 6y^2)<\/li>\n\n\n\n<li>(3y \\cdot 7 = 21y)<\/li>\n\n\n\n<li>(-4 \\cdot 2y = -8y)<\/li>\n\n\n\n<li>(-4 \\cdot 7 = -28)<\/li>\n<\/ul>\n\n\n\n<p>Combining these results gives:<\/p>\n\n\n\n<p>[<br>6y^2 + 21y &#8211; 8y &#8211; 28 = 6y^2 + (21y &#8211; 8y) &#8211; 28 = 6y^2 + 13y &#8211; 28<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Combine with the remaining terms (11y &#8211; 9)<\/h3>\n\n\n\n<p>Now, add the (11y) and (-9) to the expanded expression:<\/p>\n\n\n\n<p>[<br>6y^2 + 13y &#8211; 28 + 11y &#8211; 9<br>]<\/p>\n\n\n\n<p>Combining like terms gives:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The (y^2) term: (6y^2)<\/li>\n\n\n\n<li>The (y) terms: (13y + 11y = 24y)<\/li>\n\n\n\n<li>The constant terms: (-28 &#8211; 9 = -37)<\/li>\n<\/ul>\n\n\n\n<p>So, the entire expression simplifies to:<\/p>\n\n\n\n<p>[<br>6y^2 + 24y &#8211; 37<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Compare with the given options<\/h3>\n\n\n\n<p>Now let&#8217;s examine the options provided:<\/p>\n\n\n\n<p>A. (16y &#8211; 6)<\/p>\n\n\n\n<p>B. (6y + 11y + 19)<\/p>\n\n\n\n<p>C. (6y + 24y &#8211; 37)<\/p>\n\n\n\n<p>D. (9y &#8211; 37)<\/p>\n\n\n\n<p><strong>Checking each option:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Option A is not equivalent as it lacks a (y^2) term.<\/li>\n\n\n\n<li>Option B simplifies to (17y + 19), which does not match.<\/li>\n\n\n\n<li>Option C simplifies to (30y &#8211; 37) which is also not a match.<\/li>\n\n\n\n<li>Option D simplifies to (9y &#8211; 37), again not equivalent.<\/li>\n<\/ul>\n\n\n\n<p>The correct equivalent expression is <strong>C<\/strong>, when interpreted as (6y^2 + 24y &#8211; 37), aligning with the expanded expression. The answer can be clarified if we rephrase or consider the polynomial terms.<\/p>\n\n\n\n<p>Thus, the correct answer is:<\/p>\n\n\n\n<p><strong>C. (6y + 24y &#8211; 37)<\/strong> (interpreted in context, matching the (6y^2 + 24y &#8211; 37) upon correction).<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Which expression is equivalent to the given expression ? (3y-4) (2y+7) +11y-9 A. 16y-6 B. 6y+11y +19 C. 6y +24y-37 D. 9y-37 The Correct Answer and Explanation is: To find which expression is equivalent to ((3y &#8211; 4)(2y + 7) + 11y &#8211; 9), we need to first expand the expression ((3y &#8211; 4)(2y + [&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-152744","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/152744","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=152744"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/152744\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=152744"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=152744"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=152744"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}