Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 5 - Section 5.5 - Factoring Special Forms - Exercise Set: 43

Answer

$2x(x-y)(x+y)(x^2+y^2)$

Work Step by Step

Factor out the greatest common factor, $2x$, to obtain: $=2x(x^4-y^4) \\=2x[(x^2)^2-(y^2)^2]$ The binomial is a difference of two squares. RECALL: $a^2-b^2=(a-b)(a+b)$ Factor the difference of two squares using the formula above with $a=x^2$ and $b=y^2$ to obtain: $=2x(x^2-y^2)(x^2+y^2)$ The first binomial factor is a difference of two squares. Factor using the formula above with $a=x$ and $b=y$ to obtain: $=2x(x-y)(x+y)(x^2+y^2)$
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