Multiply A Polynomial By A Monomial

In this video, learn how to multiply a polynomial by a monomial. After you finish this lesson, view all of our Pre-Algebra lessons and practice problems.

In this video, we are going to look at how to multiply a polynomial by a monomial.
For example:
To multiply:
3x(4x^2y-3y+12xy^2)
distribute the 3x to the terms inside the parenthesis to get
12x^3y-9xy+36x^2y^2

Multiply a Polynomial by a Monomial

Examples of Multiplying a Polynomial by a Monomial

Example 1

7x^2(6x^2 + 9xy + 10y^2)

Distribute 7x^2 to each of the terms inside the parenthesis to get:

42x^4=63x^3y+10x^2y^2

Example 2

2u(6u^2- 9uv + v^2)

Distribute 2u to each of the terms inside the parenthesis to get:

12u^3 - 18u^2v + 2uv^2

Video-Lesson Transcript

This video will discuss how to multiply a polynomial by a monomial.

Let’s have an example.

We have a monomial which is 3x and a polynomial 4x^{2}y - 3y + 12xy^{2}.

Now, let’s multiply.

3x (4x^{2}y - 3y + 12xy^{2})

In order of operations, we should combine the terms inside the parenthesis first. But, we don’t have like terms in it.

So, let’s just use the distributive property to distribute the monomial to each one of the terms.

So, what we’re going to do is 3x times the first term. Then 3x times the second term. And lastly, 3x times the third term.

The answer is

12x^{3}y - 9xy + 36x^{2}y^{2}

Just a recap, to multiply a polynomial by a monomial, distribute the monomial to each term of the polynomial.