You should already be familiar with the exponent rules, and how to multiply monomials. We're going to look at how to multiply two binomials like this: (x  5)·(x + 2)
One method is called F.O.I.L., which is an acronym for 'first, outside, inside, last', the order in which you multiply corresponding terms.
But lets look a little more closely at what's going on first.


Here is a simple multiplication involving a monomial and a binomial:
x·(x + 2)
This expression means: 'multiply both terms in the bracket by x'
x·(x + 2) = x^{2} + 2x
Here's a similar question:
5·(x + 2)
This expression means: 'multiply both terms in the bracket by 5'
5·(x + 2) = 5x  10
Now let's look at this question:
(x  5)(x + 2)
This just means that you have to multiply both terms in the second bracket, first by x, and then multiply them again by 5. You will get four answers:
x^{2} + 2x  5x  10
This can be simplified, by combining the two middle terms, to:
x^{2}  3x  10
This method works fine. But there's a slightly different way to do this. It involves multiplying the four corresponding terms in a certain order. It's called the F.O.I.L. method.
The acronym 'FOIL' is just a way to help you remember which terms to multiply. It will remind you that there are four answers, and if everyone in your class uses the FOIL order, your second step will always look the same as everyone else's.
Here's how it works:

The first terms in each are x and x. Multiply them.

you get x^{2}

The outside terms in each are x and 4. Multiply them.

you get  4x

The inside terms in each are +6 and x. Multiply them.

you get + 6x

The last terms in each are +6 and  4. Multiply them.

you get  24

... and that's how you do a binomial multiplication, using the FOIL method!
Here's another one you can look at, just to make sure you've got it:

Notice that as you multiply each pair, you take the sign with the number.
For example, the outside pair you must multiply is +x and 5

Sometimes a diagram will help you visualize which pair to multiply.
Just remember to take the sign in front of each term with it, when you multiply.


Mr. Willis
