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= (x4)(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 x^{2}. 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= (x^{2} + 5x  4x  20)
Now combine like terms and you should have your answer!
y= x^{2} + x  20
Note: When writing your final answer, remember to have your variables in order from largest to smallest. That is, have x^{2} 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!
Latest tutorials

How to Be Productive
October 16th, 2017 at 12:43pm

Five Tips on How to Study More Efficiently
September 24th, 2016 at 11:01am

How to Survive Your First Year of College
August 10th, 2015 at 08:12am

How to Succeed in AP Language and Composition
June 2nd, 2014 at 04:26am

How to Improve Your GPA
May 31st, 2014 at 10:50pm