The Distributive Property

The distributive property is a very useful tool in algebra.

Here are the basics:a(b + c) = ab + ac  OR   a(b - c) = ab - ac

We can plug in some easy numbers to show that it works.

a = 5, b = 2 and c = 9

First we will use order of operations.

5(2 + 9)

5(11)

55

Now, let's see the answer if we distribute the 5 to everything in the parentheses.

5(2) + 5(9)

10 + 45

55

Either way, we get the same answer. You could try out other numbers as well and you would still get the same result.

Let's see it in action with algebra!

Example #1:5(3x + 4)

In this example, we cannot combine the terms inside the parentheses because they are not "like terms". Therefore, the only method we have to simplify this expression is the distributive property.

5(3x + 4)

5(3x) + 5(4)

15x + 20

Example #2:4(2 - 7y)

We can use the same steps when there is subtraction inside the parentheses instead of addition.

4(2 - 7y)

4(2) - 4(7y)

8 - 28y

Example 3:11 + 3(12m - 9)

Start this problem by distributing the 3 to both terms in the parentheses.

11 + 3(12m - 1)

11 + 3(12m) - 3(1)

11 + 36m - 3

36m + 11 - 3

36m + 8

We can also use the distributive property to find rewrite expressions using common factors.

Example 4:25g + 10

Here, both the 25 and the 10 have a common factor of 5.

We can think of 25 as 5 x 5.

We can think of 10 as 5 x 2.

We will pull the common 5 out to the front and the other factors go inside the parentheses.

25g+ 10 = 5(5g+ 2)

Example 5:28m - 56

We can think of 28 as 7 x 4.

We can think of 56 as 7 x 8.

Now we have 28m- 56 = 7(4m- 8)


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