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 going from the term (number or letter) on the outside of the bracket to each of the terms on the inside of the brackets. This is to ensure that you multiply the term that is outside the bracket by all of the terms on the inside of the bracket.

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

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

Before we look at an example, I am going to go through the rules for the signs 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.

Let’s start by multiplying the first term in the bracket by 4. The first term in the bracket is 2

Let’s start by multiplying the first term in the bracket by 4. The first term in the bracket is 2

*x*and when we multiply it by 4, we get 8*x*.We now multiply the second term in the bracket (7) by 4, which is 28.

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.We now multiply 4*y* by the second term inside the bracket, which is – 2*y*. The best way to multiply these terms is to multiply the signs, the numbers 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}

We now combine all of these together, which will give us the value of the second term in the expanded-out expression. The second term is -8*y*^{2}.

There are no terms that are the same in the expression above and this means that the answer is already in its 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 inside the bracket. When we are multiplying the terms, it is easier to find the sign, the number and then the unknowns. The expanded bracket is shown below.The video has a longer explanation as to how each of the terms in the expression above are obtained.

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

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