# Like Terms

*It may help you to read Introduction to Algebra first*

## 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:

7x |
x |
-2x |

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

### Example:

(1/3)xy^{2} |
−2xy^{2} |
6xy^{2} |
xy/2^{2} |

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

## Unlike Terms

If they are not like terms, they are called "**Unlike Terms**":

Unlike Terms | Why they are "Unlike Terms" | ||
---|---|---|---|

−3xy | −3y | 12y^{2} |
← these are all unlike terms (xy, y and y are all different)^{2} |

### Example: These are all **Unlike** Terms because the variables and/or their exponents are different:

2x |
2x^{2} |
2y |
2xy |

## Combining Like Terms

You can add **like terms** together to make one term:

### Example: 7**x** + **x**

They are both **like terms**, so you can just add them:

7**x** + **x** = 8**x**

### By the way ... why don't we write "1x" ?

It is just easier to write **x**. Imagine adding eggs:

**7 eggs plus 1 egg is 8 eggs**

is written **7 eggs + egg = 8 eggs**

### Example: 4**x**^{3} + 3**x**^{2} − 7 − **x**^{2} + 2

^{3}

^{2}

^{2}

Some of the terms are **like terms**.

Combine **like terms**:

(4**x ^{3}**) + (3

**x**−

^{2}**x**) + (2 − 7)

^{2}Then add **like terms**:

4**x ^{3}** + 2

**x**− 5

^{2}