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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 handy.

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

This is a model of what the algebraic expression 2(x+4) looks like using Algebra tiles.

distributive property using algebra tiles

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.

Example 1

distributive property

Example 2 is very similar to example 1 above. The only difference is the minus sign. Inside of the parenthesis, we have the expression (x-7), so notice how my answer also contains the minus sign.

Example 2

using the distributive property in algebra

In example 3, I'd just like to point out that sometimes you may have a coefficient with x. For example, inside of the parenthesis, we have the expression (4x - 5). You can still multiply 2 times 4x to get 8x.

Example 3

distributive property

For example 4, notice that we are distributing a negative number. This becomes tricky because we have to pay careful attention to our signs. Take a look.

Example 4

distributive property

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.

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