Multiplying Polynomials

Contributor: Elephango Editors. Lesson ID: 10828

Does multiplying polynomials feel like a rollercoaster ride? End those ups and downs! Rapping and online quizzes and a match game and online examples help you learn how to FOIL those polynomials!


Algebra I

learning style
Auditory, Visual
personality style
Golden Retriever
Grade Level
High School (9-12)
Lesson Type
Skill Sharpener

Lesson Plan - Get It!

  • Do you see a polynomial in this picture?

Before we begin, let's make sure you remember the definition of a polynomial!

A polynomial is a math expression that has one or more terms. A term is made up of constants, variables, and exponents.

These are examples of terms:

  4x 8 6xy 7x3


These terms are then combined by math operations - like addition, subtraction, division, or multiplication - to make up polynomials.

These are examples of terms combined to make polynomials:

4x - 86xy + 7x3 + 88(6xy)4x(8 - 7x3)(8 - 4x)(7x3 +6xy)

In this lesson, we will focus on multiplying polynomials!

If you're more of the visual learner, here is a great Unlock Math video that's just under three minutes:

Introduction to Polynomials

For even more information on polynomials, check out our lesson found under Additional Resources in the right-hand sidebar.

Okay, now back to the rollercoaster!

  • Did you find the polynomial yet?

There is one, and not just numbers hidden somewhere in the picture. When you graph polynomials, you end up with an image that looks very similar to a rollercoaster!

Now that you had a quick review of what polynomials are (and learned a neat fact about polynomials!), let's review the methods of multiplying them!

Multiplying Polynomials: one term x two- or three-term polynomial

If one of the polynomials being multiplied contains only one term, you simlply mutliply each term inside the parentheses by the single term outside of the parentheses:

one-term polynomial

Multiplying Polynomials: two-term polynomial x two-term polynomial

When multiplying two-term polynomials, you will use the FOIL (first, outer, inner, last) method.

Learn the FOIL Song to help jog your memory, and make you sing each time you see a polynomial!

FOIL Song:

Here is an example of how to multiply polynomials using FOIL:

FOIL example

Multiplying Polynomials: two-term polynomial x three-term polynomial

When multiplying two-term polynomials by three-term polynomials, the FOIL method will not work.

In this case, you will need to keep track and multiply the first term in the first polynomial by each term in the second polynomial.

step 1

Then, you will multiply the second term in the first polynomial by each term in the second polynomial.

step 2

Last, you will combine like terms together and simplify.

step 3

Now you are ready to visit Got It? to practice multiplying polynomials!

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