Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 9 - Inequalities and Problem Solving - 9.2 Intersections, Unions, and Compound Inequalities - 9.2 Exercise Set - Page 591: 96



Work Step by Step

$\bf{\text{Solution Outline:}}$ Get the $GCF$ of the given expression, $ 50c^6-18d^2 .$ Then use the factoring of the difference of $2$ squares. $\bf{\text{Solution Details:}}$ The $GCF$ of the terms is $ 2 $ since it is the highest number that can evenly divide (no remainder) all the given terms. Factoring the $GCF,$ the expression above is equivalent to \begin{array}{l}\require{cancel} 50c^6-18d^2 \\\\= 2(25c^6-9d^2) .\end{array} The expressions $ 25c^6 $ and $ 9d^2 $ are both perfect squares (the square root is exact) and are separated by a minus sign. Hence, $ 25c^6-9d^2 $ is a difference of $2$ squares. Using the factoring of the difference of $2$ squares which is given by $a^2-b^2=(a+b)(a-b),$ the expression above is equivalent to \begin{array}{l}\require{cancel} 2(25c^6-9d^2) \\\\= 2(5c^3-3d)(5c^3+3d) .\end{array}
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