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 OutsideInside 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. 

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

F:   O:   I:    L:

x • x x • 6 3 • x 3 • 6

=

x2 6x 3x 18

=

x2 + 6x + 3x + 18     x2 + 9x + 18

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

Make a grid of boxes - kind of like a tic-tac-toe board.  See right... Then, fill in the binomials as shown
Now, multiply each corresponding row and column.  Match the cells!	Now, combine 3x and 6x = 9x
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.

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