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:

F 
x • x 
= 
x^{2} 
= 

O 
x • 6 
6x 
x^{2} + 6x + 3x + 18 
I 
3 • x 
3x 
x^{2} + 9x + 18 
L 
3 • 6 
18 

This means that FOIL helps us to expand (x + 3)•(x + 6) into x^{2} + 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 tictactoe 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):
Now, multiply each corresponding row and column, then match the cells!
Now, combine 3x and 6x = 9x



You can now combine to x^{2} + 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.
