Question

unit 7 review assignment
topic 2: simplifying polynomials

1. $7x^3y(x^2y - 3x + 2) + 5x^4y$

Explanation:

Step1: Distribute the monomial

Multiply \(7x^{3}y\) with each term inside the parentheses:
\(7x^{3}y \cdot x^{2}y = 7x^{3 + 2}y^{1 + 1}=7x^{5}y^{2}\),
\(7x^{3}y \cdot (-3x)= -21x^{3 + 1}y=-21x^{4}y\),
\(7x^{3}y \cdot 2 = 14x^{3}y\).
So the expression becomes \(7x^{5}y^{2}-21x^{4}y + 14x^{3}y+5x^{4}y\).

Step2: Combine like terms

Combine the terms with \(x^{4}y\):
\(-21x^{4}y + 5x^{4}y=(-21 + 5)x^{4}y=-16x^{4}y\).

Answer:

\(7x^{5}y^{2}-16x^{4}y + 14x^{3}y\)