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 5.6 - A General Factoring Strategy - Exercise Set - Page 379: 63

Answer

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

Work Step by Step

The product of a binomial sum and a binomial difference is: $(A+B)(A-B)=A^2-B^2$. The square of a binomial sum is: $(A+B)^2=A^2+2AB+B^2$. The square of a binomial difference is: $(A-B)^2=A^2-2AB+B^2$. Hence: $a^2(x-y)+4(y-x)=\\=a^2(x-y)-4(x-y)\\=(x-y)(a^2-4)\\=(x-y)(a+2)(a-2)$
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