Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter P - Section P.4 - Polynomials - Exercise Set - Page 56: 75



Work Step by Step

The given expression can be written as: $[(3x+7)-5y][(3x+7)+5y].$ The expression above is of the form $(a-b)(a+b)$. RECALL: (1) $(a-b)(a+b) = a^2-b^2$ (2) $(a+b)^2=a^2+2ab+b^2$ Multiply the expression using formula (1) above with $a=3x+7$ and $b=5y$ to obtain: $=(3x+7)^2 - (5y)^2 \\=(3x+7)^2-25y^2$ Square the binomial using formula (2) with $a=3x$ and $b=7$ above to obtain: $=(3x)^2+2(3x)(7)+7^2-25y^2 \\=9x^2+42x+49-25y^2 \\=9x^2-25y^2+42x+49$
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