College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter P - Prerequisites: Fundamental Concepts of Algebra - Exercise Set P.5: 70

Answer

$7(x^{2}+1)(x^{2}-1)$

Work Step by Step

We are given the expression $7x^{4}-7$. First, we can use the distributive property to factor out 7, the greatest common factor of both terms. $7x^{4}-7=7(x^{4}-1)$ If $a$ and $b$ are real numbers, we know that $a^{2}-b^{2}=(a+b)(a-b)$. Therefore, $7(x^{4}-1)=7(x^{2}+1)(x^{2}-1)$. In this case, $a=x^{2}$ and $b=1$.
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