## Algebra 1: Common Core (15th Edition)

Published by Prentice Hall

# Chapter 8 - Polynomials and Factoring - Chapter Review: 20

#### Answer

$-8n^4-10n^3+18n^2$

#### Work Step by Step

We can multiply a monomial by a polynomial using the distributive property, which states that we multiply the term outside the parentheses by each term inside the parentheses and then combine like terms to simplify: $$-2n^2(5n-9+4n^2)=(-2n^2)(5n)+(-2n^2)(-9)+(-2n^2)(4n^2)=-10n^3+18n^2-8n^4$$To write in standard form, the term with the highest power must come first. This gives us: $-8n^4-10n^3+18n^2$.

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