**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.
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