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 5 - Polynomials and Factoring - 5.6 Factoring: A General Strategy - 5.6 Exercise Set: 52

Answer

$7(p^2+q^2)(p+q)(p-q)$

Work Step by Step

Factoring the $GCF= 7 $, then the given expression, $ 7p^4-7q^4 $ is equivalent to \begin{array}{l} 7(p^4-q^4) .\end{array} Using $a^2-b^2=(a+b)(a-b)$ or the factoring of the difference of $2$ squares, then the complete factored form of the expression above is \begin{array}{l} 7(p^2+q^2)(p^2-q^2) \\\\= 7(p^2+q^2)(p+q)(p-q) .\end{array}
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