## Intermediate Algebra (12th Edition)

Published by Pearson

# Chapter 4 - Section 4.4 - Multiplying Polynomials - 4.4 Exercises - Page 305: 76

#### Answer

$9m^2-12m+4+6mp-4p+p^2$

#### Work Step by Step

Using $(a+b)^2=a^2+2ab+b^2$ or the square of a binomial, the given expression, $[(3m-2)+p]^2 ,$ is equivalent to \begin{array}{l}\require{cancel} (3m-2)^2+2(3m-2)(p)+(p)^2 \\\\= (3m-2)^2+2p(3m-2)+p^2 \\\\= (3m-2)^2+6mp-4p+p^2 \\\\= [(3m)^2+2(3m)(-2)+(-2)^2]+6mp-4p+p^2 \\\\= 9m^2-12m+4+6mp-4p+p^2 .\end{array}

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