{"id":18625,"date":"2025-06-13T07:56:56","date_gmt":"2025-06-13T07:56:56","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=18625"},"modified":"2025-06-13T07:57:00","modified_gmt":"2025-06-13T07:57:00","slug":"find-the-product-of-1-5x-and-2-7-x","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/find-the-product-of-1-5x-and-2-7-x\/","title":{"rendered":"Find the product of 1.5x and (2.7-x)"},"content":{"rendered":"\n

Find the product of 1.5x and (2.7-x)<\/p>\n\n\n\n

The correct answer and explanation is:<\/strong><\/mark><\/p>\n\n\n\n

Answer:<\/strong><\/h3>\n\n\n\n

To find the product of 1.5×1.5x and (2.7\u2212x)(2.7 – x), we use the distributive property: 1.5x\u22c5(2.7\u2212x)=1.5x\u22c52.7\u22121.5x\u22c5x1.5x \\cdot (2.7 – x) = 1.5x \\cdot 2.7 – 1.5x \\cdot x<\/p>\n\n\n\n

Now calculate each term:<\/p>\n\n\n\n

    \n
  1. 1.5x\u22c52.7=4.05×1.5x \\cdot 2.7 = 4.05x<\/li>\n\n\n\n
  2. 1.5x\u22c5x=1.5×21.5x \\cdot x = 1.5x^2<\/li>\n<\/ol>\n\n\n\n

    So, the product is: 1.5x(2.7\u2212x)=4.05x\u22121.5×21.5x(2.7 – x) = 4.05x – 1.5x^2<\/p>\n\n\n\n

    \n\n\n\n

    Explanation (Approx. 300 Words):<\/strong><\/h3>\n\n\n\n

    When multiplying algebraic expressions, especially a monomial (like 1.5×1.5x) with a binomial (like 2.7\u2212x2.7 – x), we use the distributive property<\/strong>. This property allows you to “distribute” the monomial across the terms inside the parentheses.<\/p>\n\n\n\n

    In this case, the binomial has two terms: 2.7 and -x. The monomial outside the parenthesis is 1.5×1.5x. To multiply 1.5×1.5x by the binomial, you multiply it separately with each term inside the parentheses:<\/p>\n\n\n\n

      \n
    1. First Term<\/strong>: Multiply 1.5×1.5x by 2.7: 1.5x\u22c52.7=(1.5\u22c52.7)x=4.05×1.5x \\cdot 2.7 = (1.5 \\cdot 2.7)x = 4.05x Here, we multiply the numerical coefficients (1.5 and 2.7), and keep the variable xx attached.<\/li>\n\n\n\n
    2. Second Term<\/strong>: Multiply 1.5×1.5x by \u2212x-x: 1.5x\u22c5(\u2212x)=\u22121.5×21.5x \\cdot (-x) = -1.5x^2 This time, you’re multiplying the coefficients (1.5 and -1), and the variables x\u22c5x=x2x \\cdot x = x^2.<\/li>\n<\/ol>\n\n\n\n

      Now combine the two results: 4.05x\u22121.5×24.05x – 1.5x^2<\/p>\n\n\n\n

      This is the final expression for the product.<\/p>\n\n\n\n

      This expression is in standard polynomial form<\/strong>, where terms are ordered by decreasing exponents. You can also write it as: \u22121.5×2+4.05x-1.5x^2 + 4.05x<\/p>\n\n\n\n

      Both forms are mathematically equivalent. The expression represents a quadratic polynomial<\/strong>, and it’s useful in many applications like optimization problems, graphing parabolas, and modeling real-world situations.<\/p>\n","protected":false},"excerpt":{"rendered":"

      Find the product of 1.5x and (2.7-x) The correct answer and explanation is: Answer: To find the product of 1.5×1.5x and (2.7\u2212x)(2.7 – x), we use the distributive property: 1.5x\u22c5(2.7\u2212x)=1.5x\u22c52.7\u22121.5x\u22c5x1.5x \\cdot (2.7 – x) = 1.5x \\cdot 2.7 – 1.5x \\cdot x Now calculate each term: So, the product is: 1.5x(2.7\u2212x)=4.05x\u22121.5×21.5x(2.7 – x) = 4.05x […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-18625","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/18625","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=18625"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/18625\/revisions"}],"predecessor-version":[{"id":18626,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/18625\/revisions\/18626"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=18625"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=18625"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=18625"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}