# Chapter 4 - Mixed Review Exercises - Page 319: 13

$9m^2-30mn+25n^2-p^2$

#### Work Step by Step

Use special products to multiply the given expression, $[(3m-5n)+p][(3m-5n)-p] .$ Using $(x+y)(x-y)=x^2-y^2$ or the product of the sum and difference of like terms, the expression above simplifies to \begin{array}{l}\require{cancel} (3m-5n)^2-(p)^2 \\\\= (3m-5n)^2-p^2 .\end{array} Using $(x+y)^2=x^2+2xy+y^2$ or the square of a binomial, the expression above simplifies to \begin{array}{l}\require{cancel} (3m)^2+2(3m)(-5n)+(-5n)^2-p^2 \\\\= 9m^2-30mn+25n^2-p^2 .\end{array}

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