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# FOIL Method

The FOIL method is an important algebra method that defines how two binomials are multiplied. A binomial is a polynomial with two terms; and a polynomial is an expression of finite length where the variable is only affected by addition, subtraction and multiplication but not division.

An example of a polynomial is given below

A binomial expression is of the following form

where each set of parentheses is a binomial. Thus a binomial is a can be factored into a product of two binomials. Each term (each letter) is referred to as a monomial. The FOIL method is a standard algorithm for solving binomials of the form above.

FOIL is an acronym for:

First - first multiply the first term in each set of the parentheses

Outside - then multiply the outside term in each set of the parentheses

Inside - then multiply the inside term in each set of the parentheses

Last - lastly multiply the last term in each set of the parentheses

Applying the FOIL method to the expression

would result in the following

where:

ac is the product of the First terms in each set of parentheses

ad is the product of the Outside terms in each set of parentheses

bc is the product of the Inside terms in each set of parentheses

bd is the product of the Last terms in each set of parentheses

The FOIL method is the same as a two-step distributive property method and the above algorithm can be thought of as

which turns out as

## Examples of the FOIL Method

Solve the following expressions

Step 1

Step 2

Step 1

Step 2

Step 3

Step 1

Step 2

Step 1

Step 1

Step 2

### Example 6

Step 1

Step 2

Step 3

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