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Chapter 5: Problem 50

Find each product of the monomial and the polynomial. $$\left(4 x^{3}+5 x^{2}\right)(2 x)$$

Short Answer

Expert verified
The product of the monomial and the polynomial \( (4x^3 + 5x^2)(2x) \) is \( 8x^4 + 10x^3 \).

Step by step solution

01

Identify the monomial and the polynomial

In the given expression, the monomial is \(2x\) and the polynomial is \(4x^3 + 5x^2\).
02

Apply the distributive property

The distributive property states that \(a(b + c) = ab + ac\). Therefore, the monomial \(2x\) should be multiplied with each term in the polynomial. That is, \(2x * 4x^3\) and \(2x * 5x^2\).
03

Perform the multiplication operations

By multiplying the monomial with each term in the polynomial, we get \(8x^4\) and \(10x^3\). Thanks to the laws of exponents, when multiplying two powers of the same base, the exponents are added.
04

Write the final answer

The final expression obtained is the sum of these two products, \(8x^4 + 10x^3\). This is the product of the given monomial and polynomial.

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Most popular questions from this chapter

List the whole numbers in this set: $$\left\\{-4,-\frac{1}{5}, 0, \pi, \sqrt{16}, \sqrt{17}\right\\}$$

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