## Precalculus (6th Edition) Blitzer

Published by Pearson

# Chapter P - Section P.4 - Polynomials - Exercise Set: 77

#### Answer

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

#### Work Step by Step

The given expression is of the form $(a-b)(a+b)$ where $a=5y$ and $b=2x+3$ 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 to obtain: $=(5y)^2 - (2x+3)^2 \\=25y^2-(2x+3)^2$ Square the binomial using formula (2) with $a=2x$ and $b=3$ above to obtain: $=25y^2-[(2x)^2+2(2x)(3)+3^2] \\=25y^2-(4x^2+12x+9)$ Subtract each term of the trinomial to obtain: $=25y^2-4x^2-12x-9 \\=-4x^2+25y^2-12x-9$

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