# FOIL Method(KS3, Year 7)

## The Lesson

The 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 binomials 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 First Outside Inside Last.

## Question

Expand the brackets below. # 1

First: Multiply the first terms in each of the brackets together. x × x = x2 x2

# 2

Outside: Multiply the outside terms in each of the brackets together, and add to the previous result. x × 2 = 2x x2 + 2x

# 3

Inside: Multiply the inside terms in each of the brackets together, and add to the previous result. 1 × x = x x2 + 2x + x

# 4

Last: Multiply the last terms in each of the brackets together, and add to the previous result. 1 × 2 = 2 x2 + 2x + x + 2

# 5

Simplify the expression if necessary by collecting like terms together. In our example, we can collect the x terms together.
x2 + 2x + x + 2 = x2 + 3x + 2

We have used the FOIL method to expand the expression: ## Lesson Slides

The slider below shows another real example of using the FOIL method. Open the slider in a new tab

## 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 = x2
• Multiplying a variable with a variable with a coefficient.
x × 2y = 2xy 3x × x = 3x2
• Multiplying two variables with coefficients together.
2x × 3y = 6xy 3x × 5x = 15x2

## 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:
x2 + 3x + 2
This suggests that if the reverse process takes place, some quadratic equations can be written as two brackets mulitplied together:
(x + a)(x + b)
This is known as factoring a quadratic equation, and is of great help when solving quadratic equations.
Help Us To Improve Mathematics Monster