Multiply Out Double Brackets and Simplify

In algebra, when we multiply out brackets, everything inside the bracket gets multiplied by whatever is outside the bracket.

Take care with the signs, remembering the rules about multiplying negative numbers:

When multiplying or dividing numbers, if the signs are the same (+ and + or - and -) the answer is positive (+)

If the signs are different (+ and - or - and +) the answer is negative (-)

The following examples show how the 3 and the -5 outside the brackets affect the terms inside the brackets.

In this activity, we are going to multiply out double brackets and then collect like terms together,

Example

Multiply out the brackets and simplify by collecting like terms.

3(4x - 2) - 5(2x + 3)

Answer

With the first bracket: multiply everything inside the bracket by 3: 

3 x 4x = 12x

3 x -2 = -6

With the second bracket, multiply everything inside the bracket by -5:

-5 x 2x = -10x

-5 x 3 = -15

From the breakdown above we get:

12x - 6 - 10x - 15

Now collect the x terms to get 12x - 10x = 2x and the numbers to get -6 - 15 = -21

The answer is 2x - 21

Let's try some questions now.