Distributive Property

How does it work?

Suppose you have an expression like 2(x + 3). This means 2 multiplied by everything inside the brackets (x + 3). In order to simplify this expression you'll first need to get rid of the brackets by multiplying the 2 onto everything inside the brackets first.

This is called the distributive property.

So 2(x + 3) is the same as 2x + 2(3) OR 2x + 6. The multiplication has be distributed to the addition.

Here's a model showing the equation. If you have 2 groups of x + 3 you can see that it would be equal to 2x + 6.

The most common mistake is to just multiply the 2 over the first number in the brackets and not the second. For example, multiply the 2 by the x but not by the 3.

Examples

Example 1

Simplify -3(x - 4)

Solution:

-3(x - 4)

= -3(x) - 3(-4)

= -3x + 12

First multiply the -3 times the x and the -3 times -4

Simplify by multiplying out

Make sure you follow your integer rules when doing these types of problems. Remember, two negatives multiplied by each other makes a positive number.

Example 2

Simplify -(x - 2)

Solution:

Remember that this is the same as -1(x - 2). The 1 is implied even though it does not need to be written.

-1(x - 2)

= -1(x) - 1(-2)

= -1x + 2 or -x + 2

First multiply the -1 times x, then multiply -1 times -2.

Simplify the multiplication

Example 3

Simplify 2(2x + 1)

Solution:

2(2x + 1)

=2(2x) + 2(1)

=4x + 2