I don't understand the FOIL method at all. Could someone please explain it to me in extremely simple terms? Thanks.

Concepts: The word FOIL is simply an acronym for the method of multiplying
binomials.

It stands for:

F irst (multiply the first term of each binomial together)
O uter (multiply the two outside terms together)
I nner (multiply the two inside terms together)
L ast (multiply the last term of each binomial together)

For instance, let's look at (x 2 +3)(x-2)

F irst (x 2 )(x)=x 3
O uter (x 2 )(-2)=-2x 2
I nner (3)(x)=3x
L ast (3)(-2)=-6

Now that we have all the terms, we can add them together in descending
order of the power of the variable.

Then we get:
(x 2 +3)(x-2)=x 3 -2x 2 +3x-6

There, we have multiplied the two binomials into a polynomial. Using the FOIL method, you will be more likely to remember how to multiply binomials, and as a result, show a better understanding of the Happy FOILing!

Here is a website that discusses this further:

FOILing

I don't exactly understand what Sherasi is saying, so I'll just show you the way I have taught it.

FOIL stands for
First terms
Outside terms
Inside terms
Last terms

In the problem of multiplying the two values,
(2x + 3) and (x - 2) (These are said as "two x plus three" and "x minus two".), you must identify which are the First terms, the Outside terms, the Inside terms, and the Last terms. It may help if you see the problem this way: (2x+3)(x-2)

First terms - You find this by looking at the first terms inside each parenthesis. In this problem, the First terms are 2x and x. ( 2x + 3) and (x - 2)

Outside terms - You find these by looking at each term that is on the outside of the two values when they are together like this: (2x+3)(x-2). The Outside terms here are 2x and -2. (2x + 3) and (x-2).

Inside Terms - The Inside terms are the ones that are inside the Outside terms. In this problem, they are 3 and x. (2x3)(x-2)

Last terms - The Last terms are the ones that are last inside each parenthesis. In this problem, they are 3 and -2. (2x3)(x-2)

Now let's do the multiplying.

First Terms.... 2x times x = 2x²
Outside terms.... 2x times -2 = -4x
Inside terms..... 3 times x = 3x
Last terms.... 3 times -2 = -6

Now let's put this on one line: 2x² -4x +3x -6

Combine like terms: 2x² -x -6