Intermediate Algebra (12th Edition)

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

Chapter 5 - Chapters R-5 - Cumulative Review Exercises - Page 364: 25



Work Step by Step

$\bf{\text{Solution Outline:}}$ Use the Distributive Property and then combine like terms to simplify the given expression, $ (3x^3+4x^2-7)-(2x^3-8x^2+3x) .$ $\bf{\text{Solution Details:}}$ Using the Distributive Property which is given by $a(b+c)=ab+ac,$ the expression above is equivalent to \begin{array}{l}\require{cancel} (3x^3+4x^2-7)-1(2x^3-8x^2+3x) \\\\= (3x^3+4x^2-7)-1(2x^3)-1(-8x^2)-1(3x) \\\\= 3x^3+4x^2-7-2x^3+8x^2-3x .\end{array} Combining like terms results to \begin{array}{l}\require{cancel} (3x^3-2x^3)+(4x^2+8x^2)-3x-7 \\\\ x^3+12x^2-3x-7 .\end{array}
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