How to FOIL

FOIL is an acronym used in mathematics which stands for Firsts Outers Inners Lasts. It is a process used to multiply polynomials of two terms together. A polynomial is a sum of terms, and a term is just a constant (any number) multiplied by a variable (some unknown number). An example of a polynomial would be 5x + 2, where 5x and 2 are the terms of the polynomial. FOILing is a fundamental mathematical skill used throughout algebra, calculus, and other high level math courses.

In order to complete this process, you should be able to add multiply.

You will need:

• Paper
• Pencil
• Two polynomials consisting of two terms to multiply

It typically takes around 3 minutes to complete this process.

In this example we will multiply together two simple polynomials, x+1 and x+2.

Start by multiplying the first term of each polynomial together. In this case the first term for each is x, so we will multiply x times x.

Next, we will multiply the terms on the outside of the two polynomials. In this case, an x and a 2 are on the outside, so we multiply x times 2.

Now we will multiply the terms on the inside (1 and x).

Lastly, we will multiply the last term of each polynomial together to obtain 1 times 2 equals 2.

Add the terms we obtained together to get our answer.

Now we want to add like terms together to obtain the simplest answer possible. In this case we will add 2x and x together to obtain 3x.

Note:

We were able to add 2x and x (notice: x = 1*x) together because both terms are a number multiplied by x. We could not have added x and 3 together because 3 does not have an x attached to it.

You have now successfully multiplied two polynomials together to obtain a new polynomial by FOILing.

If you found this Instructable interesting, you might also enjoy:

• Factoring: https://www.instructables.com/id/How-to-factor/
• Multiplying fractions: https://www.instructables.com/id/Multiplying-Fract...
• Graphing: https://www.instructables.com/id/How-to-Graph/

Khan Academy also has many helpful math videos on its YouTube channel: https://www.youtube.com/user/khanacademy