# 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**

### Example 1

**Step 1**

**Step 2**

### Example 2

**Step 1**

**Step 2**

**Step 3**

### Example 3

**Step 1**

**Step 2**

### Example 4

**Step 1**

### Example 5

**Step 1**

**Step 2**

### Example 6

**Step 1**

**Step 2**

**Step 3**