# Combining ("Gathering") Like Terms

The
**
terms of an expression
**
are the parts of a mathematical expression that are separated by a plus (+) or minus (–) sign.

Each term is either a number or the product of a number (sometimes an understood $1$ ) and one or more variables.

For Example,

$6x+4y-2x+2$

The four terms of the above expression are $6x$ , $4y$ , $-2x$ and $2$ .

**
Like Terms:
**

Terms are
**
like terms
**
if their variable parts are the same.

For example:

$4x+18y-3x-7x+3xy$

In the above expression $4x$ , $-3x$ and $-7x$ are like terms. $18y$ and $3xy$ are unlike terms.

Like terms can be added or subtracted using the
Distributive Property
. The variable part stays the same; we just add the
**
coefficients
**
(the numerical portion of the terms). Unlike terms cannot be added or subtracted.

**
Example:
**

Simplify $12a+3b-8b-8a+a-7b$ .

Rearrange and group like terms using the Commutative and Associative Properties.

$\left(12a-8a+a\right)+\left(3b-8b-7b\right)$

Use the Distributive Property to combine like terms.

$\left(12-8+1\right)a+\left(3-8-7\right)b$

$=5a-12b$