Beginning Algebra
Tutorial 28: Multiplying Polynomials
Learning Objectives
After completing this tutorial, you should be able to:
 Multiply any polynomial times any other polynomial.
 Use the FOIL method to multiply a binomial times a binomial.

Introduction
In this tutorial we help you expand your knowledge of
polynomials by
looking at multiplying polynomials together. We will look at
using
the distributive property,
initially shown in Tutorial 8: Properties of Real Numbers, to
help
us out. Again, we are using a concept that you have already seen
to apply to the new concept. After going through this tutorial
you
should have multiplying polynomials down pat. 
Tutorial
On this page we will look at some of the more common
types of polynomials
to illustrate this idea. 
In this case, there is only one term in each
polynomial. You
simply multiply the two terms together. 
Example
1: Find the following product . 
In this case, there is only one term in one
polynomial and more
than one term in the other. You need to distribute the monomial
to
EVERY term of the other polynomial. 
Example
2: Find the following product . 
In this case, both polynomials have two terms.
You need to
distribute both terms of one polynomial times both terms of the other
polynomial.
One way to keep track of your distributive property
is to
Use the FOIL method. Note that this method
only works
on (Binomial)(Binomial).
F

First terms

O

Outside terms

I

Inside terms

L

Last terms

This is a fancy way of saying take every term of the
first binomial
times every term of the second binomial. In other words, do the
distributive
property for every term in the first binomial. 
Example
3: Find the following product . 

*Use the FOIL method
*Combine like terms

Example
4: Find the following product . 

*Rewrite as base
(3y  2) times
itself
*Use the FOIL method
*Combine like terms

As mentioned above, use the distributive property
until every term
of one polynomial is multiplied times every term of the other
polynomial.
Make sure that you simplify your answer by combining any like terms. 
Example
5: Find the following product . 

*Use Dist. Prop. twice
*Combine like terms

Practice Problems
These are practice problems to help bring you to the
next level.
It will allow you to check and see if you have an understanding of
these
types of problems. Math works just like
anything
else, if you want to get good at it, then you need to practice
it.
Even the best athletes and musicians had help along the way and lots of
practice, practice, practice, to get good at their sport or instrument.
In fact there is no such thing as too much practice. To get the most out of these, you should work the
problem out on
your own and then check your answer by clicking on the link for the
answer/discussion
for that problem. At the link you will find the answer
as well as any steps that went into finding that answer. 
Practice
Problems 1a  1d: Find the following products.
Need Extra Help on these Topics?
Last revised on August 2, 2011 by Kim Seward.
All contents copyright (C) 2001  2011, WTAMU and Kim Seward. All rights reserved.

