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.