# 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.

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

$=5a-12b$