The FOIL

method

When do you use the FOIL method?

FOIL IS USED WHEN DISTRIBUTING TWO BINOMIALS

(x+3)(x+7)

Example of when you use FOIL:

FOIL stands for…

How you use the FOIL methodBack to our example (x+3)(x+7)

The first step of foil is “first” which means multiplying the first terms of

each of the binomials

In this example the first terms are “x” and “x” so multiplying them

together would equal “x2”

The next step of FOIL is “outer” so you now multiply the outermost

terms togetherIn our example of (x+3)(x+7) the outer

most terms are “x” and “7” so multiplying those together equals “7x”

Once you get an answer you add it to the previous answer you got. In this

case we add “7x” to “x2” so we now have “x2+7x”

“Inner” is the next step of our method which means you multiply together the innermost two terms

“3” and “x” are our innermost two terms in our example (x+3)(x+7) so

together they equal “3x”

Once again we add this answer to our previous answer so we now have

“x2+7x+3x”

The next step of FOIL is “last” so you now multiply the terms which occur last in both of our binomials

Because you got another answer you again add that to our previous answers. In this case you get

“x2+7x+3x+21”

Since “3” and “7” are the terms that occur last in our binomials your last answer you

get is “21”

The last step of the FOIL method is to simply

AFTER STARTING WITH (X+3)(X+7) WE WENT THROUGH THE STEPS OF FOIL AND ARE NOW

LEFT WITH “X2+7X+3X+21” SO WE NOW COMBINE LIKE TERMS.

THE ONLY LIKE TERMS IN THIS EXAMPLE ARE “7X” AND “3X” SO AFTER

COMBINING THEM YOU GET YOUR FINAL ANSWER WHICH IS

“X2+10X+21”