Intermediate Algebra for College Students (7th Edition)

Published by Pearson

Chapter 5 - Section 5.5 - Factoring Special Forms - Exercise Set - Page 372: 73

Answer

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

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: $z^2-(x^2-4xy+4y^2)=\\=(z)^2-((x)^2+2\cdot2y\cdot x+(2y)^2)=\\=(z)^2-(x-2y)^2\\=(z-x+2y)(z+x-2y)$

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