Algebraic terms can, and often should, be combined and simplified. However, only terms that are "like", meaning that they have the exact same variables in each of them, can be added or subtracted. Furthermore, the variables have to have the same exponent to be "like"; xy^{2} and xy are not like terms, since y is squared in the first term.

**Combining like terms **is pretty simple, as long as you are careful with your negative and positive numbers. (For a quick review, check out adding integers and subtracting integers.) When adding and subtracting like terms, all you really need to do is combine the coefficients.

**Look Out:** you can only combine terms with the exact same variables with the same exponents!

It can seem a little more complicated when dealing with subtraction. You must be extremely careful to keep the operations with the correct terms. In the example:

there are two terms that can be combined (2y and 8y). However, it is *"minus 8y"* and we MUST be careful to keep the subtraction sign. 2y – 8y = -6y. This expression simplifies to:

It is also worthy to note that the order of addition does not matter. This expression could also be written as 5x +-6y or 5x – 6y.

In each example below, we will draw shapes around the like terms

## Combining Like Terms Practice:

Simplify: | |

There are only two terms in this expression that are like: 3xy and -6xy. | |

is , so our simplified expression will be: | |

Simplify: | |

The parentheses in this expression are not necessary, since it doesn't change how we treat each expression. We can rewrite it without these. | |

The tricky part with this problem is to keep the correct addition and subtraction signs with each term. Notice that it is , and also . | |

Simplify: | |

There are two things to be careful with in this problem. First, each term in the second expression is being subtracted, so we must "distribute" the subtraction sign to each term when removing the parentheses. | |

Notice also that when we distribute the subtraction to another subtraction, it becomes addition. The second thing we need to be cautious with is the last term, b. Even though it doesn't show a coefficient, it is the same as 1b. | |

Our simplified expression is: | |

Simplify:

Hint

there are two sets of like terms

Answer

Simplify:

Hint

-1 and 9 are also like terms

Answer

Simplify:

Hint

two negative signs make a positive

Answer

Simplify:

Answer