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: 69



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