{"id":224017,"date":"2025-06-02T15:54:50","date_gmt":"2025-06-02T15:54:50","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=224017"},"modified":"2025-06-02T15:54:52","modified_gmt":"2025-06-02T15:54:52","slug":"did-cherise-use-algebra-tiles-to-correctly-represent-the-product-of","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/02\/did-cherise-use-algebra-tiles-to-correctly-represent-the-product-of\/","title":{"rendered":"Did Cherise use algebra tiles to correctly represent the product of"},"content":{"rendered":"\n

Did Cherise use algebra tiles to correctly represent the product of (x \u00e2\u20ac\u201c 2)(x \u00e2\u20ac\u201c 3)? No, she did not multiply the x-tiles by the negative integer tiles correctly. No, she did not multiply the negative integer tiles by the other negative integer tiles correctly. No, she did not add the terms together correctly. Yes, the product is x^2 \u00e2\u20ac\u201c 5x \u00e2\u20ac\u201c 6.<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

The correct answer is:
Yes, the product is x2\u22125x+6x^2 – 5x + 6,<\/strong> not x2\u22125x\u22126x^2 – 5x – 6.
So Cherise did not use the algebra tiles correctly.<\/strong>
The correct option is:
No, she did not multiply the negative integer tiles by the other negative integer tiles correctly.<\/strong><\/p>\n\n\n\n

\n\n\n\n

Explanation<\/h3>\n\n\n\n

When using algebra tiles to multiply two binomials such as (x\u22122)(x\u22123)(x – 2)(x – 3), each part of the expression is represented visually. Algebra tiles typically include:<\/p>\n\n\n\n

    \n
  • Large square tiles<\/strong> to represent x2x^2,<\/li>\n\n\n\n
  • Rectangular tiles<\/strong> to represent xx or \u2212x-x, and<\/li>\n\n\n\n
  • Small square tiles<\/strong> to represent constants like 11 or \u22121-1.<\/li>\n<\/ul>\n\n\n\n

    To represent the product (x\u22122)(x\u22123)(x – 2)(x – 3), you arrange one binomial horizontally and the other vertically to form a rectangle.<\/p>\n\n\n\n

    Step-by-step process:<\/h4>\n\n\n\n
      \n
    1. Set up the expression<\/strong>:
      Horizontal edge: x\u22122x – 2 \u2192 one xx-tile and two \u22121-1-tiles.
      Vertical edge: x\u22123x – 3 \u2192 one xx-tile and three \u22121-1-tiles.<\/li>\n\n\n\n
    2. Multiply the tiles<\/strong>:\n
        \n
      • x\u22c5x=x2x \\cdot x = x^2 \u2192 one x2x^2-tile.<\/li>\n\n\n\n
      • x\u22c5\u22123=\u22123xx \\cdot -3 = -3x \u2192 three \u2212x-x-tiles.<\/li>\n\n\n\n
      • \u22122\u22c5x=\u22122x-2 \\cdot x = -2x \u2192 two \u2212x-x-tiles.<\/li>\n\n\n\n
      • \u22122\u22c5\u22123=6-2 \\cdot -3 = 6 \u2192 six<\/strong> +1+1-tiles (because a negative times a negative is positive).<\/li>\n<\/ul>\n<\/li>\n\n\n\n
      • Combine like terms<\/strong>:
        x2\u22123x\u22122x+6=x2\u22125x+6x^2 – 3x – 2x + 6 = x^2 – 5x + 6<\/li>\n<\/ol>\n\n\n\n

        If Cherise got x2\u22125x\u22126x^2 – 5x – 6, she incorrectly calculated the constant term<\/strong> by treating \u22122\u22c5\u22123-2 \\cdot -3 as \u22126-6 instead of +6+6. This shows she made a sign error<\/strong> in multiplying the two negative integers, which is a common mistake when working with algebra tiles or binomial multiplication.<\/p>\n\n\n\n

        So, the correct answer is:
        No, she did not multiply the negative integer tiles by the other negative integer tiles correctly.<\/strong><\/p>\n\n\n\n

        \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

        Did Cherise use algebra tiles to correctly represent the product of (x \u00e2\u20ac\u201c 2)(x \u00e2\u20ac\u201c 3)? No, she did not multiply the x-tiles by the negative integer tiles correctly. No, she did not multiply the negative integer tiles by the other negative integer tiles correctly. No, she did not add the terms together correctly. Yes, […]<\/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-224017","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/224017","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=224017"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/224017\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=224017"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=224017"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=224017"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}