# Adding and Subtracting Polynomials

A polynomial looks like this:

example of a polynomial

this one has 3 terms

To add polynomials we simply add any **like terms** together ... so what is a like term?

## Like Terms

Like Terms are **terms** whose variables (and their exponents such as the 2 in x^{2}) are the same.

In other words, terms that are "like" each other.

Note: the **coefficients** (the numbers you multiply by, such as "5" in 5x) can be different.

### Example:

**x**

**x**

**x**

**x**

are all **like terms** because the variables are all **x**

### Example:

**xy**

^{2}**xy**

^{2}**xy**

^{2}**xy**/2

^{2}are all **like terms** because the variables are all **xy ^{2}**

### Example: These are **NOT** like terms because the variables and/or their exponents are different:

**x**

**x**

^{2}**y**

**xy**

## Adding Polynomials

Two Steps:

- Place
**like terms**together - Add the like terms

### Example: Add **2x**^{2} + 6x + 5 and **3x**^{2} - 2x - 1

^{2}+ 6x + 5

^{2}- 2x - 1

^{2}+ 6x + 5 + 3x

^{2}− 2x − 1

^{2}+3x

^{2}+ 6x−2x + 5−1

^{2}+ (6−2)x + (5−1)

^{2}+ 4x + 4

Here is an animated example:

*(Note: there was no "like term" for the -7 in the other polynomial, so we didn't have to add anything to it.*)

## Adding in Columns

We can also add them in columns like this:

## Adding Several Polynomials

We can add several polynomials together like that.

### Example: Add **(2x**^{2} + 6y + 3xy) , **(3x**^{2} - 5xy - x) and **(6xy + 5)**

^{2}+ 6y + 3xy)

^{2}- 5xy - x)

Line them up in columns and add:

^{2}+ 6y + 3xy

3x

^{2}- 5xy - x

__6xy + 5__

^{2}+ 6y + 4xy - x + 5

Using columns helps us to match the correct terms together in a complicated sum.

## Subtracting Polynomials

To subtract Polynomials, first **reverse the sign of each term** we are subtracting (in other words turn "+" into "-", and "-" into "+"), **then add** as usual.

Like this:

*Note: After subtracting 2xy from 2xy we ended up with 0, so there is no need to mention the "xy" term any more.*