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A detailed tutorial on the solving of problems using the binomial theorem. Stepby step tutorial including several examples of how to solve problems using the binomial theorem for reference.

The binomial theorem is something you should all be familiar with – it is the alternative to the F.O.I.L. technique. It is used when you are given a binomial that is raised to a power. The simplest version of it is expressed like this:

This can also be expressed as a factorial notation, in the form:

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Description

This video shows the correct way to multiply binomials together using the FOIL technique. A helpful hint for seeing if you matched up the terms correctly is given in the video. Content is laid out in an organized manner.

Overview

FOIL is a basic math function that stands for First, Outside, Inside, Last. It is like the Order of Operations – it gives you a set order to solve problems in. FOIL is used when you multiply two binomials together. Binomials are sets of parenthesis that have two added or subtracted numbers with variables in them. Here is an example of a problem that would need FOIL:

(a + b) (x – y)

You would use FOIL to multiply together different parts of the problem. We will highlight the parts of the problem in their correct order:

First: (a + b) (x – y)

Outside: (a + b) (x – y)

Inside: (a + b) (x – y)

Last: (a + b) (x - y)

Notice that the addition and subtraction signs are grouped with the last term in each set of parenthesis – this is very important if you expect to get the right answer. So, our problem can be simplified by writing it this way:

(a + b) (x – y) = (a * x) + (a * -y) + (b * x) + (b * -y)