What Is the FOIL Method?

What Is the FOIL Method?

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:

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The slider below shows another real example of using the FOIL method.

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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