The FOIL method is a commonly used technique for multiplying two binomials (a binomial is a polynomial with two terms). FOIL is an acronym that stands for:

First term in each binomial
Outer term in each binomial
Inner term in each binomial
Last term in each binomial

Here is an example:

(6x+2)(2x-3)

Let’s try and multiply these binomials together using FOIL.

Start by multiplying the First terms.

(6x+2)(2x-3)

6x*2x

12x²

Next, we’ll multiply the Outer terms…

(6x+2)(2x-3)

12x²+6x*-3

12x²-18x

and the Inner terms…

(6x+2)(2x-3)

12x²-18x+2*2x

12x²-18x+4x

Finally, let’s multiply the Last terms.

(6x+2)(2x-3)

12x²-18x+4x+2*-3

12x²-18x+4x-6

After the First, Outer, Inner, and Last terms have been multiplied together, combine the like terms (-18x and 4x) to get the final answer:

12x²-14x-6