### Learning Objectives

- Add polynomials
- Use horizontal and vertical organization to add polynomials

## Add polynomials

Adding and subtracting **polynomials** may sound complicated, but it’s really not much different from the addition and subtraction that you do every day. The main thing to remember is to look for and combine **like terms**.

You can add two (or more) polynomials as you have added algebraic expressions. You can remove the parentheses and combine like terms.

### Example

Add. [latex]\left(3b+5\right)+\left(2b+4\right)[/latex]

When you are adding polynomials that have subtraction, it is important to remember to keep the sign on each term as you are collecting like terms. The next example will show you how to regroup terms that are subtracted when you are collecting like terms.

### Example

Add. [latex]\left(-5x^{2}–10x+2\right)+\left(3x^{2}+7x–4\right)[/latex]

The above examples show addition of polynomials horizontally, by reading from left to right along the same line. Some people like to organize their work vertically instead, because they find it easier to be sure that they are combining like terms. The example below shows this “vertical” method of adding polynomials:

### Example

Add. [latex]\left(3x^{2}+2x-7\right)+\left(7x^{2}-4x+8\right)[/latex]

Sometimes in a vertical arrangement, you can line up every term beneath a like term, as in the example above. But sometimes it isn’t so tidy. When there isn’t a matching like term for every term, there will be empty places in the vertical arrangement.

### Example

Add. [latex]\left(4x^{3}+5x^{2}-6x+2\right)+\left(-4x^{2}+10\right)[/latex]

You may be thinking, how is this different than combining like terms, which we did in the last section? The answer is, it’s not really. We just added a layer to combining like terms by adding more terms to combine. :) Polynomials are a useful tool for describing the behavior of anything that isn’t linear, and sometimes you may need to add them.

In the following video, you will see more examples of combining like terms by adding polynomials.

In the next section we will subtract polynomials.