# FOIL (First, Outer, Inner and Last) Method

FOIL (the acronym for first, outer, inner and last) method is an efficient way of remembering how to multiply two binomials in a very organized manner. The word FOIL is an acronym that stands for:

To put this in perspective, suppose we want to multiply two arbitrary binomials, **( a + b)(c + d)**.

- The
**first**means that we multiply the terms which occur in the first position of each binomial.

- The
**outer**means that we multiply the terms which are located in both ends (outermost) of the two binomials when written side-by-side.

- The
**inner**means that we multiply the middle two terms of the binomials when written side-by-side.

- The
**last**means that we multiply the terms which occur in the last position of each binomial.

- After obtaining the four (4) partial products coming from the
**first**,**outer**,**inner**and**last**, we simply add them together to get the final answer.

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

**Example 1**: Multiply the binomials **( x + 5)(x − 3)** using the FOIL Method.

- Multiply the pair of terms coming from the
**first**position of each binomial.

- Multiply the
**outer**terms when the two binomials are written side-by-side.

- Multiply the
**inner**terms when the two binomials are written side-by-side.

- Multiply the pair of terms coming from the
**last**position of each binomial.

- Finally, simplify by combining like terms. I see that we can combine the two middle terms with variable
*x*.

**Example 2**: Multiply the binomials **(3 x − 7)(2x + 1)** using the FOIL Method.

If the first presentation on how to multiply binomials using FOIL doesn’t make sense yet. Let me show a different way. The idea is to expose you to different ways on how to address the same type of problem with a different approach.

After applying the FOIL, we arrive at this polynomial which we can simplify by combining similar terms. The two middle x-terms can be subtracted to get a single value.

**Example 3**: Multiply the binomials **(–4 x + 5)(x + 1)** using the FOIL Method.

Another way of doing this is to list the four partial products, and then add them together to get the answer.

Get the sum of the partial products, and then combine similar terms.

**Example 4**: Multiply the binomials **(–7 x −3)(-2x + 8)** using the FOIL Method.

**Solution**:

Finally, combine like terms to finish this off!

**Example 5**: Multiply the binomials **(– x − 1)(–x + 1)** using the FOIL Method.

**Solution**:

Notice that the middle two terms cancel each other out!

**Example 6**: Multiply the binomials **(6 x + 5)(5x + 3)** using the FOIL Method.

**Solution**:

Add the two middle x-terms, and we are done!

**Example 7**: Multiply the binomials **( x − 12)(2x + 1)** using the FOIL Method.

**Solution**:

After expanding the binomials, combine like terms to get the final answer!

**Example 8**: Multiply the binomials **(–10 x − 6)(4x − 7)** using the FOIL Method.

**Solution**:

After distributing the terms of the two binomials using the FOIL method, combine like terms to get the final answer.