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:

a plus b times c plus d 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:

First Outside Inside Last

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.
x plus 1 times x plus 2

Step-by-Step:

1

First: Multiply the first terms in each of the brackets together.

Firsts. x times x
x × x = x2 x2

2

Outside: Multiply the outside terms in each of the brackets together, and add to the previous result.

Outsides. x times 2
x × 2 = 2x x2 + 2x

3

Inside: Multiply the inside terms in each of the brackets together, and add to the previous result.

Insides. 1 times x
1 × x = x x2 + 2x + x

4

Last: Multiply the last terms in each of the brackets together, and add to the previous result.

Lasts. 1 times 2
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

Answer:

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.
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See Also

What is algebra? What is a term? Multiplying letters Multiplying terms Collecting like terms What is a quadratic equation? Factoring quadratic equations Solving quadratic equations