Using the Distributive Property

The distributive property is used A LOT in Algebra! It is essential that you MASTER this skill in order to solve algebraic equations.

First we are going to make sure that you have the proper background knowledge, so let's look at a simple math problem:

2( 3+4) = ?
2( 7) = 14

Since this problem contains all numerals, we can use the order of operations and solve inside the parenthesis first. We know that 3 + 4 = 7 and then multiply 7 by 2 and we get our answer of 14! That's basic math.

But, in Algebra we often don't know one of the numeric values and a variable (letter) is used in it's place. Let's look at another example:

2(x+4) = ?

In this problem, we don't know the value of x, so we can't add x + 4. But... we do want to simplify it a little further by removing the parenthesis. So, this is when the distributive property comes in!

To prove that this property works, look at the model below.

distributive property

The problem 2(x+4) means that you multiply the quantity (x +4) by 2. You could also say that you add x+4, 2 times which is the way it is shown in the model. You can see we got an answer of 2x +8 using the models.

We would get the same answer using the distributive property! Let's take a look.

distributive property example

Here's a couple of other examples for you to study. Copy the examples onto your paper and do them with me.

More Examples

distributive property in algebra

distributive property examples

TIP: When you simplify algebraic expressions, you DO NOT want two math symbols following each other!

For example: -3x + (-4) is incorrect. See how the plus sign is followed by the negative sign? This is better read as -3x - 4.

-3x - (-4) is incorrect. See how the minus sign is followed by the negative sign? This is better read as -3x + 4.

If you have two math symbols following each other, change the math sign to it's opposite (plus to minus or minus to plus)and change the negative sign following to a positive!

Subtracting a negative is the same as adding a positive.

Adding a negative is the same as subtracting a positive.

distributive property practice problems

Click here to try some practice problems.

If you are ready, you can also move onto simplifying algebraic expressions!


We would love to hear what you have to say about this page!

Algebra Tools - Unit 1

Like Us on Facebook

Recommend this on Google

Algebra Class E-course Members


Sign Up for Algebra Class E-courses

Click here to renew or retrieve a lost password.

Search This Site

Custom Search

Do You Need Help With Your Basic Algebra Skills?

Get access to your FREE Algebraic Expressions E-course. You'll have instant access to video lessons, practice problems, quizzes, and read more....

It's FREE, so try it today!

sign up

Having Trouble with Your Homework?


Need a Tutor?

Find a Local Tutor Today

[ ?]

Subscribe To This Site

Add to Google
Add to My Yahoo!
Add to My MSN
Add to Newsgator
Subscribe with Bloglines

Enjoy This Site?
Then why not use the button below, to add us to your favorite bookmarking service?

| Homepage | Contact Me | Privacy Policy | Disclaimer |Affiliates

Return to top
By Karin Hutchinson Copyright© 2009-2013.