Tutoring math, the FOIL method is used daily.  We’ll explain it here.

In math, the distributive property is used constantly.  An illustration:

3(5x-7)=15x-21

To see what’s really happening here, look to the following:

We see that we take the outer number (in this case, 3) and multiply it by each term in the brackets, writing the result each time.

A binomial is a couple of terms that cannot be added. In the above example, 5x-7 is a binomial. When two binomials are multiplied together, it might look like this:

In order to multiply a binomial by a binomial, notice the steps below:

(The letters stand for First, Outer, Inner, Last: hence the acronym FOIL)

F: 2x times 4x gives 8x²
O: 2x times 9 gives 18x
I: -5 times 4x gives -20x
L: -5 times 9 gives -45

Writing the terms consecutively, we get

8x² + 18x -20x -45

Now, we can combine the 18x with the -20x to finally obtain

8x² -2x -45.

Indeed, (2x-5)(4x+9) = 8x² -2x -45.

To verify the FOIL method, try it on (12)(10), written as

(10 +2)(9 + 1)

F: 10(9)=90
O: 10(1)=10
I: 2(9)=18
L: 2(1)=2

90 + 10 + 18 + 2 = 120, which of course we know is the answer to (12)(10).

Hope this helps.

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC