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 5.2 - Multiplication of Polynomials - Exercise Set - Page 338: 89

Answer

$25y^2-4x^2-12x-9$

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: $[5y+(2x+3)][5y-(2x+3)]=(5y)^2-(2x+3)^2=25y^2-(2x)^2-2\cdot2x \cdot3-3^2=25y^2-4x^2-12x-9$
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