# FOIL Method For Multiplying Two Binomials

FOIL Method is a technique that enables us to multiply two binomials in a very simple and easy way. But before explaining this method, it is necessary to recall the definition of binomial. A binomial is a special case of a polynomial, which is an algebraic expression consisting of only two terms separated by one of the + or - signs.  ## FOIL method mathematically

Foil method is a technique that makes it easier for a beginner student to remember the steps of the expanding process for an algebraic expression consisting of the product of two binomial terms written as follows:

The F-O-I- L acronym stands for First, Outer, Inner, and Last.

Let’s explain each of these terms:

• F: the first, that is, we multiply the first two terms from each parenthesis:
• O: the outers, ths is, we multiply the outermost terms of the two binomials:
• I: the inners, that is, we multiply the innermost terms of the two binomials:
• L: the last, that is, we multiply the last two terms from each parenthesis:

When we get the four sums, we simplify like terms by Combining Like Terms.

### Note:

Let , , and a real numbers.

### Warning!

Pay attention to the sign of the numbers , , and in the above formula.

## Examples of How to Multiply Binomials using the FOIL Method

#### Example1:

Distribute and simplify the expression below using FOIL method:

#### Solution:

• First: multiply the first two terms from each binomial:
• Outer: we multiply the outermost terms of the two binomials:
• Inner: we multiply the innermost terms of the two binomials:
• Last: multiply the last two terms from each binomial:

Having applied the FOIL method, now we simplify the expression obtained using Combining Like Terms.

We have: and are like terms, hence:

#### Example2:

Distribute and simplify the expression below using FOIL method:

#### Solution:

• First: multiply the first two terms from each binomial:
• Outer: we multiply the outermost terms of the two binomials:
• Inner: we multiply the innermost terms of the two binomials:
• Last: multiply the last two terms from each binomial:

Having applied the FOIL method, now we simplify the expression obtained using Combining Like Terms.

We have: and are like terms, hence:

#### Example3:

Distribute and simplify the expression below using FOIL method:

#### Solution:

• First: multiply the first two terms from each binomial:
• Outer: we multiply the outermost terms of the two binomials:
• Inner: we multiply the innermost terms of the two binomials:
• Last: multiply the last two terms from each binomial:

Having applied the FOIL method, now we simplify the expression obtained using Combining Like Terms.

We have: and are like terms, hence:

#### Example4:

Distribute and simplify the expression below using FOIL method:

#### Solution:

• First: multiply the first two terms from each binomial:
• Outer: we multiply the outermost terms of the two binomials:
• Inner: we multiply the innermost terms of the two binomials:
• Last: multiply the last two terms from each binomial:

Having applied the FOIL method, now we simplify the expression obtained using Combining Like Terms.

We have: and are like terms, hence:

#### Example5:

Distribute and simplify the expression below using FOIL method:

#### Solution:

• First: multiply the first two terms from each binomial:
• Outer: we multiply the outermost terms of the two binomials:
• Inner: we multiply the innermost terms of the two binomials:
• Last: multiply the last two terms from each binomial:

Having applied the FOIL method, now we simplify the expression obtained using Combining Like Terms.

We have: and are like terms, hence:

#### Example6:

Distribute and simplify the expression below using FOIL method:

#### Solution:

• First: multiply the first two terms from each binomial:
• Outer: we multiply the outermost terms of the two binomials:
• Inner: we multiply the innermost terms of the two binomials:
• Last: multiply the last two terms from each binomial:

We don't have like terms in this expression, hence:

#### Example7:

Distribute and simplify the expression below using FOIL method:

#### Solution:

• First: multiply the first two terms from each binomial:
• Outer: we multiply the outermost terms of the two binomials:
• Inner: we multiply the innermost terms of the two binomials:
• Last: multiply the last two terms from each binomial:

Having applied the FOIL method, now we simplify the expression obtained using Combining Like Terms.

We have: and are like terms, hence:

#### Example1:

Distribute and simplify the expression below using FOIL method:

#### Solution:

• First: multiply the first two terms from each binomial:
• Outer: we multiply the outermost terms of the two binomials:
• Inner: we multiply the innermost terms of the two binomials:
• Last: multiply the last two terms from each binomial:

We don't have like terms in this expression, hence: