## Precalculus (6th Edition) Blitzer

Published by Pearson

# Chapter P - Section P.4 - Polynomials - Exercise Set - Page 56: 74

#### Answer

$x^2+2xy+y^2-25$

#### Work Step by Step

The given expression can be written as $[(x+y)+5][(x+y)-5].$ 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 $a=x+y$ and $b=5$ to obtain: $=(x+y)^2 - 5^2 \\=(x+y)^2-25$ Square the binomial using formula (2) with $a=x$ and $b=y$ above to obtain: $=x^2+2xy+y^2-25$

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