**Example 1**

Expand the brackets below.

I am going to use the FOIL method (First, Outside, Inside and Last) to expand these double brackets. The first step in the FOIL method is to multiply the first term in each of the brackets together; we therefore multiply *x* by *x*, which gives us *x*^{2}.

The next step in the FOIL method is to multiply the outside terms, which means that we multiply *x* and 4, which gives us 4*x*.

We are now onto the I in FOIL, which stands for inside. This means that we multiply 3 and *x*, which gives 3*x*.

We are now onto the last part of FOIL, which is the L and this stands for the last terms. This means that we are multiplying 3 by 4, which gives us 12.

The final step is to simplify and collect any like terms. There are 3 different types of terms in this expression; these different terms are *x*^{2}, *x* and numbers. There are two different terms in the expression that contain *x*’s (4*x* and 3*x*). We are able to combine these two terms to give us 7*x*. This results in the expression becoming:

The FOIL method is a good way to ensure that we multiply out double brackets correctly.

**Example 2**

Let’s multiply out the brackets below.

I am going to be using the FOIL method (First, Outside, Inside and Last). This means that I will be multiplying out the first terms in each of the two brackets, which is *x* and 2*x*. When we are multiplying out these two terms, you may find it easier to split it up into the signs, numbers and then unknowns (only *x*’s in this case). Both of the terms that we are multiplying are positive, which means that the answer will be positive. We now multiply the numbers; 1 multiplied by 2, which is 2. Finally, we multiply the *x*’s; *x* multiplied by *x* is *x*^{2}. Therefore, the first term is 2*x*^{2}.

*x*from the first bracket and -4 from the second bracket. We are multiplying a positive by a negative, which will give us a negative. For the numbers, we are multiplying 1 by 4, which is 4. And there is one

*x*. All of this together means that the outside terms multiplied together is -4

*x*.

*x*. Both of these terms are positive, thus means that the answer will be positive. We are then multiplying 4 by 2, which gives us 8. Finally, there is an

*x*from the second bracket. All of this together results in the inner terms multiplied together being 8

*x*.

We now need to make sure that we have simplified the answer. There is only one term that has *x*^{2} in it and one term that only has numbers in it. However, there are two terms that contain *x* in and we can combine these terms. When we are combining the terms, we need to be careful about the signs that come before the terms. The two terms that we are combining are -4*x* and 8*x*, which when combined is 4*x *(-4*x* + 8*x* = 4*x*). The simplified expression is:

**Example 3**

Expand and simplify the bracket below.

Like the question before, I am going to use the FOIL method.

We multiple the **First** terms first: 3*y* x 2*y* = 6*y*^{2}

Next, we multiply the terms on the **Outside** of the brackets: 3*y* x (-4) = -12*y*

Wen then multiply the terms on the **Inside** of the brackets: (-2) x 2*y* = -4*y*

Finally, we multiply the **Last** terms in each of the brackets: (-2) x (-4) = 8

We combine all of these values to give us:

*y*in; we can collect -12

*y*and -4

*y*together, which results in -16

*y*. This results in the expression becoming.