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!



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