Adding and Subtracting Polynomials

Now that you have studied some of the definitions related to polynomials, it is time to start working with polynomials. We will start with adding and subtracting polynomials.

The first thing we have to explore is how to combine like terms. When you want to add or subtract two terms (known as combining the terms) you have to make sure you are working with like terms.

When adding or subtracting terms, it is important to remember the following rule:

You can only combine like terms.

We'll try to illustrate this concept with a picture.

Examine the expression 3a + 8a. Both 3a and 8a are like terms, so they can be combined (added or subtracted). Imagine this situation as a picture:

If we were to combine the 3 a's and the 8 a's above the line, we would get:

So, three a's and eight a's make eleven a's.

Now let's see an example of trying to combine unlike terms. Look at the expression 3a + 8b. 3a and 8b are NOT like terms. Examine the diagram below:

If you try to combine the a's and b's, you just get a confused muddle of a's and b's:

You STILL have 3 a's and 8 b's, no matter how you count them! You CANNOT combine terms that are NOT like terms.

What would you like to do now?

• I would like to see examples of ADDING polynomials.
• I would like to see examples of SUBTRACTING polynomials. (Includes the Distributive Law)
• I would like to see some practice questions involving both adding and subtracting of polynomials.
• I want to go BACK to the polynomial main page.