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Chapter 5: Problem 43

Find each product of the monomial and the polynomial. $$4 x^{2}(x+2)$$

Short Answer

Expert verified
The product of the monomial and the polynomial \(4x^{2}(x+2)\) is \(4x^{3} + 8x^{2}\).

Step by step solution

01

Identify the terms

Identify the monomial and binomial terms in the problem. Here the monomial is \(4x^{2}\) and the binomial is \((x+2)\). The aim is to find the product of these two.
02

Apply the Distributive Property

The distributive property states that for any numbers \(a, b\) and \(c\), we have \(a(b + c) = ab + ac\). Applying this property to \(4x^{2}(x+2)\) gives \(4x^{2} * x + 4x^{2} * 2\).
03

Simplify the terms

Simplify the terms by completing the multiplication. Here, \(4x^{2} * x\) becomes \(4x^{3}\) and \(4x^{2} * 2\) becomes \(8x^{2}\).
04

Write the final answer

The final product of the monomial and the polynomial is \(4x^{3} + 8x^{2}\).

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