Which sum or difference is modelled by the algebra tiles? The figure shows the elimination of four red tiles and four blue tiles in which two tiles numbered with 1, two tiles with a minus square of x, and two tiles with x.<\/p>\n\n\n\n
A. (x^(2) + 4x – 2) + (x^(2) – 2x – 4) = 2x^(2) + 2x + 2<\/p>\n\n\n\n
B. (x^(2) + 4x – 2) + (x^(2) + 2x + 4) = 2x^(2) + 2x + 2<\/p>\n\n\n\n
C. (x^(2) + 4x – 2) – (-x^(2) + 2x – 4) = 2x^(2) + 2x +<\/p>\n\n\n\n
The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n The correct answer is:<\/p>\n\n\n\n A. (x\u00b2 + 4x – 2) + (x\u00b2 – 2x – 4) = 2x\u00b2 + 2x – 6<\/strong><\/p>\n\n\n\n However, this doesn’t match the result given in A<\/strong>, which states the answer is 2x\u00b2 + 2x + 2<\/strong>. This indicates a mismatch between the expressions and their calculated result.<\/p>\n\n\n\n Let\u2019s break this down carefully.<\/p>\n\n\n\n Algebra tiles are a visual method to model expressions. Typically:<\/p>\n\n\n\n In the described figure, it says:<\/p>\n\n\n\n So, the figure shows:<\/p>\n\n\n\n Hence, the remaining expression is:<\/p>\n\n\n\n 2x\u00b2 + 0x + 0 = 2x\u00b2<\/strong><\/p>\n\n\n\n This contradicts the answer provided in all the options.<\/p>\n\n\n\n Let\u2019s analyze each option:<\/p>\n\n\n\n (x\u00b2 + 4x – 2) + (x\u00b2 – 2x – 4)<\/p>\n\n\n\n Add like terms:<\/p>\n\n\n\n So, the sum is: 2x\u00b2 + 2x – 6<\/strong><\/p>\n\n\n\n This is NOT 2x\u00b2 + 2x + 2<\/strong>, so Option A is incorrect.<\/p>\n\n\n\n (x\u00b2 + 4x – 2) + (x\u00b2 + 2x + 4)<\/p>\n\n\n\n Add like terms:<\/p>\n\n\n\n Sum: 2x\u00b2 + 6x + 2<\/strong><\/p>\n\n\n\n Not 2x\u00b2 + 2x + 2<\/strong>, so Option B is incorrect.<\/p>\n\n\n\n (x\u00b2 + 4x – 2) – (-x\u00b2 + 2x – 4)<\/p>\n\n\n\n Distribute the negative sign:<\/p>\n\n\n\n Combine like terms:<\/p>\n\n\n\n Final result: 2x\u00b2 + 2x + 2<\/strong><\/p>\n\n\n\n This matches<\/strong> the result shown.<\/p>\n\n\n\n Algebra tiles are a powerful visual aid in understanding the addition and subtraction of polynomials. Each type of tile represents a term in the expression: large square tiles for $x^2$, rectangular tiles for $x$, and small square tiles for constants like +1 or -1. Positive values are usually colored blue, while negative values are red.<\/p>\n\n\n\n In this case, the diagram shows the elimination (cancellation) of equal numbers of red and blue tiles, meaning pairs like $+x$ and $-x$, or $+1$ and $-1$, are being removed. After eliminating 4 red and 4 blue tiles (which likely include 2 +x and 2 -x, and 2 +1 and 2 -1), the only visible tiles remaining are 2 $x^2$ tiles, meaning we are left with $2x^2$.<\/p>\n\n\n\n Now, let\u2019s analyze Option C:<\/p>\n\n\n\n (x\u00b2 + 4x – 2) – (-x\u00b2 + 2x – 4)<\/p>\n<\/blockquote>\n\n\n\n First, apply the distributive property<\/strong> to remove the parentheses in the subtraction:<\/p>\n\n\n\n Next, combine like terms:<\/p>\n\n\n\n This results in:<\/p>\n\n\n\n $2x^2 + 2x + 2$<\/p>\n<\/blockquote>\n\n\n\n This matches the expression modeled by the tiles. Thus, Option C<\/strong> correctly represents the sum shown in the algebra tile<\/p>\n","protected":false},"excerpt":{"rendered":" Which sum or difference is modelled by the algebra tiles? The figure shows the elimination of four red tiles and four blue tiles in which two tiles numbered with 1, two tiles with a minus square of x, and two tiles with x. A. (x^(2) + 4x – 2) + (x^(2) – 2x – 4) […]<\/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-213778","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/213778","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=213778"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/213778\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=213778"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=213778"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=213778"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\n\n\n\nInterpreting Algebra Tiles<\/h3>\n\n\n\n
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\n\n\n\nOption A:<\/h3>\n\n\n\n
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\n\n\n\nOption B:<\/h3>\n\n\n\n
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\n\n\n\nOption C:<\/h3>\n\n\n\n
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\n\n\n\n\u2705 Correct Answer: C. (x\u00b2 + 4x – 2) – (-x\u00b2 + 2x – 4) = 2x\u00b2 + 2x + 2<\/strong><\/h3>\n\n\n\n
\n\n\n\nExplanation (300+ words):<\/h3>\n\n\n\n
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