# Chapter 8 - Polynomials and Factoring - 8-2 Multiplying and Factoring - Practice and Problem-Solving Exercises - Page 495: 38

$9m^{2}n^{3}(m^{2}n^{2}-3)$

#### Work Step by Step

List the prime factors of each term. Identify the factors common to all terms. $9m^{4}n^{5}=(3\cdot 3)\cdot(m\cdot m)\cdot m\cdot m\cdot(n\cdot n\cdot n)\cdot n\cdot n$ $-27m^{2}n^{3}=-1\cdot(3\cdot 3)\cdot 3\cdot(m\cdot m)\cdot(n\cdot n\cdot n)$ GCF=$9m^{2}n^{3}$ $9m^{4}n^{5}-27m^{2}n^{3}\qquad...$factor out the GCF $=9m^{2}n^{3}(m^{2}n^{2})-9m^{2}n^{3}(3)\qquad ...$ apply the Distributive Property. $=9m^{2}n^{3}(m^{2}n^{2}-3)$

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