Answer
$(x-y)^{2}(x-y+2)(x-y-2)$
Work Step by Step
$(x-y)^{4}-4(x-y)^{2}=$... factor out $(x-y)^{2}$
$=(x-y)^{2}[(x-y)^{2}-4]$
... the brackets hold a difference of squares
$=(x-y)^{2}[(x-y)+2]\cdot[(x-y)-2]$
= $(x-y)^{2}(x-y+2)(x-y-2)$
Precalculus (6th Edition) Blitzer
by Blitzer, Robert F.
Published by
Pearson
ISBN 10:
0-13446-914-3
ISBN 13:
978-0-13446-914-0
Chapter P - Section P.5 - Factoring Polynomials - Exercise Set - Page 69: 111
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