Adding Polynomials

Before you start adding polynomials, make sure you have read and understand the explanation of why you may only combine like terms. This rule is so important, we will say it again:

You may only combine (add or subtract) LIKE TERMS.

You should also know your signed numbers. With that being said, look at the first example:

Example 1

Add the polynomial 3a + 4b to the polynomial 7a + 2b.

Solution

First, we will write this question out as a proper mathematical expression:

(3a + 4b) + (7a + 2b)

This is the form in which questions will normally be asked. First, you should look inside each set of brackets to see if there is any combining to be done - which there is not. You can remove the brackets if there is either nothing or just a plus sign out front. (You'll see something different in the next lesson on subtracting polynomials.) Removing both sets of brackets leaves us with:

3a + 4b + 7a + 2b

Now you are ready to combine like terms. This question essentially boils down into two seperate questions: 3a + 7a and 4b + 2b. So, 3a + 7a = 10a and 4b + 2b = 6b. You end up with the expression:

10a + 6b

This is your solution.

Example 2

Simplify the following expression: 3x² - 2x + 9 - x² + 7x - 12

Solution

One way to organize a question like this is to rewrite the expression grouping all of the like terms. This means to rewrite the expression writing all of the like terms beside one another, as shown below:

3x² - x² - 2x + 7x + 9 - 12

Now combine (add or subtract) the like terms in the expression above to get:

2x² + 5x - 3

This is your final answer.

Now that you have seen some examples of adding polynomials, you can move on to subtracting polynomials, head back to the adding and subtracting polynomials start page, or head back to the polynomials main page.