Binomials

A Binomial is a mathematical expression consisting of two terms connected by a plus sign or minus sign.

A term is a combination of numbers and variables. In the example 3x + 5, our first term is 3x, and our second term is 5. Terms are separated by either addition or subtraction. In our first example, notice how the 3x and 5 are separated by addition. In the last example, we have a binomial whose two terms both have the same variable s. Notice how each term has its variable to a different exponent. The first term has an exponent of 5, and the second term has an exponent of 4. While we can have fractions for our numbers, we cannot have fractional exponents.

All of these examples in the block below are binomials.

The following is a list of what binomials must have:

• They must have two terms.
• If the variables are the same, then the exponents must be different.
• Exponents must be whole positive integers. They cannot be negatives or fractions.

Binomial Theorem

What happens when you multiply a binomial by itself ... many times?

Here is the answer:

Don't worry ... I will explain it all!

And you will learn lots of cool math symbols along the way.

Binomial

A binomial is a polynomial with two terms:

Example of a Binomial

Multiplying

The Binomial Theorem shows what happens when you multiply a binomial by itself (as many times as you want).

It works because there is a pattern ... let us see if we can discover it.