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: 66

Answer

$(x-6-y)(x-6+y)$

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: $x^2-12x+36-y^2=x^2-2\cdot6\cdot x+6^2-y^2=\\=(x-6)^2-y^2\\=(x-6-y)(x-6+y)$
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