Intermediate Algebra (12th Edition)

Published by Pearson
ISBN 10: 0321969359
ISBN 13: 978-0-32196-935-4

Chapter 4 - Section 4.4 - Multiplying Polynomials - 4.4 Exercises - Page 304: 21



Work Step by Step

Using $(a+b)(c+d)=ac+ad+bc+bd$ or the FOIL Method, the product of the binomials in the given expression, $ 4x^3(x-3)(x+2) ,$ is \begin{array}{l}\require{cancel} 4x^3[x(x)+x(2)-3(x)-3(2)] \\\\= 4x^3[x^2+2x-3x-6] \\\\= 4x^3[x^2-x-6] .\end{array} Using $a(b+c)=ab+ac$ or the Distributive Property, the product of the expression above is \begin{array}{l}\require{cancel} 4x^3(x^2)+4x^3(-x)+4x^3(-6) \\\\= 4x^5-4x^4-24x^3 .\end{array}
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