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 378: 22



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 here: $32x^4y-2y^5=\\=2y(16x^4-y^4)\\=2y((4x^2)^-(y^2)^2)\\=2y(4x^2+y^2)(4x^2-y^2)\\=2y(4x^2+y^2)((2x)^2-y^2)\\=2y(4x^2+y^2)(2x+y)(2x-y)$
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