The
Please tell us using

**FOIL**stands for the**First Outside Inside Last**method. The FOIL method is a method for multiplying two brackets together. Two brackets multiplying each other are shown below: Each of the brackets**(a + b)**and**(c + d)**have two terms added (or subtracted) to each other. They are called**bi**nomials because they each have**two**terms. The FOIL method gives the order to multiply the terms together:## How to Use the FOIL Method

Using the FOIL method to expand two brackets is easy. Just remember**F**irst**O**utside**I**nside**L**ast.## Question

Expand the brackets below.## Step-by-Step:

## 1

**F**irst: Multiply the

**f**irst terms in each of the brackets together.

*x × x = x ^{2}*

**x ^{2}**

## 2

**O**utside: Multiply the

**o**utside terms in each of the brackets together, and add to the previous result.

*x × 2 = 2x*x

^{2}

**+ 2x**

## 3

**I**nside: Multiply the

**i**nside terms in each of the brackets together, and add to the previous result.

*1 × x = x*x

^{2}+ 2x

**+ x**

## 4

**L**ast: Multiply the

**l**ast terms in each of the brackets together, and add to the previous result.

*1 × 2 = 2*x

^{2}+ 2x + x

**+ 2**

## 5

Simplify the expression if necessary by collecting like terms together. In our example, we can collect the

**x**terms together.
x

^{2}**+ 2x + x**+ 2 = x^{2}**+ 3x**+ 2## Answer:

We have used the FOIL method to expand the expression:## Multiplication Tips

- Multiplying a number with a variable.
2 × x = 2x 5 × x = 5x
- Multiplying a number with a variable with a coefficient.
2 × 2x = 4x 3 × 5x = 15x
- Multiplying a variable with a variable.
x × y = xy x × x = x
^{2} - Multiplying a variable with a variable with a coefficient.
x × 2y = 2xy 3x × x = 3x
^{2} - Multiplying two variables with coefficients together.
2x × 3y = 6xy 3x × 5x = 15x
^{2}

## The FOIL Method and Factoring

In the example on this page, two brackets containing**x**'s are multiplied together.
(x + 1)(x + 2)

Using the FOIL method results in a quadratic equation:
x

This suggests that if the reverse process takes place, some quadratic equations can be written as two brackets mulitplied together:
^{2}+ 3x + 2
(x + a)(x + b)

This is known as factoring a quadratic equation, and is of great help when solving quadratic equations.
## You might also like...

algebra curriculumexpanding double bracketsmultiplying expressions in algebraexpanding double brackets using the grid method

#### Help Us Improve Mathematics Monster

- Do you disagree with something on this page?
- Did you spot a typo?

__this form__.

#### Find Us Quicker!

- When using a search engine (e.g., Google, Bing), you will find Mathematics Monster quicker if you add
**#mm**to your search term.

#### Share This Page

If you like Grammar Monster (or this page in particular), please link to it or share it with others.

If you do, __please tell us__. It helps us a lot!

#### Create a QR Code

Use our handy widget to create a QR code for this page...or any page.