**Learning Objectives**

After completing this tutorial, you should be able to:

- Identify a term, coefficient, constant term, and like terms.
- Combine like terms.
- Simplify an expression using distributive property and combining like terms.

** Introduction**

In this tutorial we will be looking at various
components of terms.
Then we will move on to adding like terms together. Some of these
concepts are based on ideas that were covered in earlier
tutorials.
A lot of times in math you are using previous knowledge to learn new
concepts.
The trick is to not reinvent the wheel each time, but recognize what
you
have done before and draw on that knowledge to help you work through
the
problems.

** Tutorial**

Examples of terms are , , , *z*

Here are the coefficients of the terms listed above:

Examples of constant terms are 4, 100, and -5.

One example of like terms is . Another example is .

It is like counting apples and oranges. **You
just count up how
many variables you have the same and write the number in front of
the common variable part.**

It looks like it. Both terms have the same
variable part, *a*.

It looks like it. Two terms have the same variable
part, *b*.
The other pair of terms are constant terms that can be combined
together.

It looks like we have two terms that have an *x* squared that we can combine and we have two terms that have an *x *that
we can combine. The poor 5 does not have anything it can combine
with so it will have to stay 5.

**Grouping like terms together and combining them we
get:**

Basically, when you have a negative sign in front of a
( ), like this
example, you can think of it as taking a -1 times the ( ). What
you
end up doing in the end is taking the opposite of every term in the ( ).

Add 3*a* + 9 to 7*a* - 2.

Basically we will be adding these two expressions
together.

**Writing this as an algebraic expression we get:**

**Regrouping and combining like terms we get:**

The sum of 5 times a number and 2, subtracted from 12 times a number.

**Writing this as an algebraic expression we get:**

**Using the** **distributive
property (found in Tutorial 8: Properties of Real Numbers)
and
then combining like terms we get:**

** 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 Problem 1a:Simplify by combining like terms.

Practice Problems 2a - 2b:Simplify the expressions.

Practice Problem 3a:Write the following as an algebraic expression and simplify if possible.

3a. The sum of 9 times a number and 5, subtracted
from 4 times
a number.

(answer/discussion to 3a)

(answer/discussion to 3a)

** Need Extra Help on these Topics?**

**The following are webpages
that can assist
you in the topics that were covered on this page: **

**http://www.purplemath.com/modules/polydefs.htm#Combining**

This webpage goes over combining like terms.

**http://www.mathleague.com/help/algebra/algebra.htm#combiningliketerms**

This webpage goes over combining like terms.

**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 26, 2011 by Kim Seward.

All contents copyright (C) 2001 - 2010, WTAMU and Kim Seward. All rights reserved.