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: 88

Answer

$49x^2+70xy+25y^2-4$

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: $[(7x+5y)-2][(7x+5y)+2]=(7x+5y)^2-(2)^2=(7x)^2+2\cdot 7x \cdot 5y+(5y)^2-4=49x^2+70xy+25y^2-4$
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