Multiplying a Binomial by a Monomial

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  • 0:04 Monomials and Binomials
  • 0:49 How to Multiply a…
  • 2:01 Lesson Summary
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Lesson Transcript
Instructor: Betsy Chesnutt

Betsy teaches college physics, biology, and engineering and has a Ph.D. in Biomedical Engineering

To multiply mathematical expressions with only one term (monomials) and mathematical expressions with two terms (binomials), you can use the distributive property of algebra. In this lesson, you will learn how it works.

Monomials and Binomials

To begin, let's review what monomials and binomials are and how we can write them. A monomial is a mathematical expression with just one term. The prefix mono tells you there is only one term in a monomial. Mono always means one, like in the words monotone, meaning one sound, and monochrome, meaning one color. That one term can contain numbers (both positive and negative) and variables with positive exponents, but no negative exponents or variables in the denominator.

examples of monomials

In contrast, the prefix bi tells you that there are two terms in a binomial. Just like a bicycle has two wheels and binoculars have two lenses, a bionomial is made up of two monomials added or subtracted from each other.

The prefix bi always means two. Just like bicycles and binoculars are made up of 2 parts, a binomial has 2 terms
bicycles, binoculars, binomials

How to Multiply a Monomial and Binomial

In many mathematical operations, it is necessary to multiply monomials and binomials. To do this, you need to use the distributive property of algebra.

Let's start with a simple example:

3(5 + 2x)

The distributive property tells you how to multiply a single term (a monomial) and two or more terms inside parentheses. It says that you can remove the parentheses in this expression by multiplying the monomial outside the parentheses by each term inside the parentheses:

monomial multiplication example 1

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