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Chapter 5: Problem 45

Find each product of the monomial and the polynomial. $$2 y^{2}\left(y^{2}+3 y\right)$$

Short Answer

Expert verified
The resulting expression after distributing the monomial \(2y^2\) over the polynomial \(y^2 + 3y\) is \(2y^4 + 6y^3\).

Step by step solution

01

Identify the terms

Identify the monomial and the polynomial in the given expression. The monomial here is \( 2y^2 \) and the polynomial is \( y^2+3y \).
02

Distribute the monomial

Next, apply the distributive property: multiply each term inside the parenthesis by the monomial.
03

Solve each multiplication

Multiply \( 2y^2 \) with each term inside the parenthesis. This gives \( 2y^2*y^2 \) and \( 2y^2*3y \).
04

Simplify

Simplify each multiplication. \( 2y^2*y^2 = 2y^4 \) and \( 2y^2*3y = 6y^3 \)

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