When we expand brackets, we multiply the term that is outside the bracket by each of the terms that are inside the bracket. After we have expanded the bracket, we need to make sure that we have given our answer in it’s simplest form.

When you are expanding brackets, you may find it easier to draw arrows that are going from the term (number or letter) on the outside of the brackets to each term inside the brackets. This is to ensure that you multiply the term that is outside the bracket by every term that is inside the bracket.

Before we look at an example, I am going to go through the rules when we are multiplying numbers or unknowns:

When you are expanding brackets, you may find it easier to draw arrows that are going from the term (number or letter) on the outside of the brackets to each term inside the brackets. This is to ensure that you multiply the term that is outside the bracket by every term that is inside the bracket.

Before we look at an example, I am going to go through the rules when we are multiplying numbers or unknowns:

**Example 1**

Expand the bracket below.

In the above expression, we are going to be multiplying all of the terms that are inside the bracket by 4.

There are no like terms in this expression, which means that we have the expression in it's simplest form.

**Example 2**

Expand the bracket below.

In the above expression, we are going to be multiplying all of the terms that are inside the bracket by 4

Multiplying 4

*y*. The best way to multiply the terms inside the brackets by 4*y*is to multiply the terms inside by 4 and then by*y*.Multiplying 4

*y*by the first term in the bracket is fairly straightforward.However, we need to be careful when we are multiplying 4

*y*by the second term in the bracket, which is -2*y*. The best way to multiply these terms out is to multiply the sign, the number and then the unknowns.- The sign – we are multiplying a positive by a negative, which means that the answer is going to be negative.
- The number – we are multiply 4 by 2, which is 8
- The
*y*’s – we are multiplying*y*by*y*, which is going to be*y*^2

*y*^2.There are no terms that are the same in the expressions above and this means that the answer is already in it's simplest form.

**Example 3**

Expand out the bracket below.

To expand out this bracket, we are going to be multiplying 4

*x*by the three different terms in the bracket. When we are multiplying the brackets out, we will find the sign, the number and then the unknowns (there are two unknowns;*x*and*y*).See the video for a longer explanation as to how each of the terms in the expression above were found.

There are no terms that are the same, which means that the expression above has been given in its simplest form.

There are no terms that are the same, which means that the expression above has been given in its simplest form.