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 - Page 372: 102



Work Step by Step

The product of a binomial sum and a binomial difference is: $(A+B)(A-B)=A^2-B^2$. Hence here: $x^8+15x^4-16=\\=x^8-x^4+16x^4-16\\=x^4(x^4-1)+16(x^4+1)\\=(x^4-1)(x^4+16)\\=(x^4+16)((x^2)^2-1^2)\\=(x^4+16)(x^2-1)(x^2+1)\\=(x^4+16)(x^2-1^2)(x^2+1)\\=(x^4+16)(x+1)(x-1)(x^2+1)$
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