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: 69

Answer

$(3x-5-6y)(3x-5+6y)$

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: $9x^2-30x+25-36y^2=\\=(3x)^2-2\cdot5\cdot3x+5^2-(6y)^2=\\=(3x-5)^2-(6y)^2\\=(3x-5-6y)(3x-5+6y)$
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