Simplifying Binomials Using FOIL What the heck is FOIL?

FOIL is a simple acronym used to solve binomials. The acronym is really easy to remember, and goes like this:

First Outside Inside Last

Easy, right? Alright, now, let's solve a binomial using FOIL.

Using FOIL in equations

Let's say you have to solve for y in this equation:

y= (x-4)(x+5)

Now, we can solve for y easily by using FOIL. The first part of FOIL, is, well, First. So, we'll multiply the first components in each set of parenthesis, which both happen to be x. As you should know, multiplying two xs together gets you x2. The second part of FOIL is Outside. So, we'll multiply the outer components of each set of parenthesis, x and 5, to give us 5x. Next, is Inside. Multiply the inner two, -4 and x, to give us -4x. We end FOIL with Last, which means the last component in each set of parenthesis. In this equation, that happens to be -4 and 5. Multiply those two together to give you -20. After using FOIL, your equation should now look like this:

y= (x2 + 5x - 4x - 20)

y= x2 + x - 20

Note: When writing your final answer, remember to have your variables in order from largest to smallest. That is, have x2 first, then x, and then your constant (the number without a variable next to it).

Another type of problem

Let's look at another type of problem that usually seems to confuse people:

y= (x - 8)2

Do not distribute the square. All you have to do in these types of problems is rewrite it like so:

y= (x - 8)(x - 8)

Now you can use FOIL like above, and get to solving!

If you think this method is too hard or confusing, by no means am I telling you this is the only way! If you find another way that is simpler for you, use it! Math is all about finding simple ways for you to understand, but FOIL is generally pretty easy for students in any type of math to understand.

I hope this tutorial cleared any confusion about solving binomials. Happy solving!