**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.
- Use special product rules to multiply a binomial squared and a product of a sum and difference of two terms

** 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 5: 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, 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).

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.

***Use the FOIL method**

***Combine like terms**

**Special Product Rule for **

**a Binomial Squared: **

Any time you have a binomial squared you can use this shortcut method to find your product.

This is a special products rule. It would be perfectly ok to use the foil method on this to find the product. The reason we are showing you this form is that when you get to factoring, you will have to reverse your steps. So when you see , you will already be familiar with the product it came from.

*****

***Write in desc. order**

This is another special products rule. It would
be perfectly
ok to use the foil method on this to find the product. The reason
we are showing you this form is that when you get to factoring, you
will
have to reverse your steps. So when you see a difference of two
squares,
you will already be familiar with the product it came from.

***Write in desc. order**

***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 - 1e:Multiply.

** Need Extra Help on these Topics?**

**http://www.algebrahelp.com/lessons/simplifying/distribution/**

This website helps with the distributive property.

**http://www.algebrahelp.com/lessons/simplifying/foilmethod/**

This website helps with the FOIL method and (polynomial)(polynomial).

**http://www.purplemath.com/modules/polymult.htm**

This webpage helps with multiplying polynomials.

**Go to Get
Help Outside the
Classroom found in Tutorial 1: How to Succeed in a Math Class for
some
more suggestions.**

Last revised on July 14, 2011 by Kim Seward.

All contents copyright (C) 2001 - 2011, WTAMU and Kim Seward. All rights reserved.