The Math Foil System

You have probably heard of the math foil system... now you need to really learn what it is and how to use it. 

FOIL is an acronym that stands for First Outside Inside Last. 

These four words remind you of the four terms that you must multiply together in order to expand a binomial multiplied by a binomial. 

In most cases your result is a trinomial, but special circumstances will cause the result to be another binomial as well.

(x + 3)(x + 6)

binomial times binomial


FIRST:  Multiply the first term of each binomial. x x

OUTSIDE:  Multiply the two terms on the outside:  x • 6

INSIDE:  Multiply the two terms on the inside:  3 • x

LAST:  Multiply the last term of each binomial:  3 • 6

Visual Representation of the Math Foil System

See a a more detailed example below:

The Math Foil System
x x
x • 6
x2 + 6x + 3x + 18
3 • x
  x2 + 9x + 18
3 • 6

This means that FOIL helps us to expand (x + 3)(x + 6) into x2 + 9x + 18.

A GradeA Trick:  If you don't like FOIL, try the Box Method

To use the box method, create grid similar to a tic-tac-toe board. See the example below. Once you have the grid, fill in the binomials across the top and the left side (they can go in either order):

Foil Math

Now, multiply each corresponding row and column, then match the cells!

Foil Box

Now, combine 3x and 6x = 9x

Learn to Foil



You can now combine to x2 + 9x + 18 just like we did before!

Hopefully this method will make it easier for you to foil.  It gives you a more concrete understanding of the math foil system.

Explore other free algebra topics or return to the GradeA homepage.



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