# Combining ("Gathering") Like Terms with Exponents

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,

$3{x}^{2}y+2xy-9x+2$

The four terms of the above expression are $3{x}^{2}y$ , $2xy$ , $-9x$ and $2$ .

**
Like Terms:
**

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

For Example,

$7{x}^{3}-14{x}^{2}-8x-3{x}^{3}+9$

In the above expression $7{x}^{3}$ , and $-3{x}^{3}$ are like terms. $-14{x}^{2},8x$ and $9$ 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 $6{x}^{2}+5x+4-4{x}^{2}+7x-8$

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

$\left(6{x}^{2}-4{x}^{2}\right)+\left(5x+7x\right)+\left(4-8\right)$

Use the Distributive Property to combine like terms.

$\left(6-4\right){x}^{2}+\left(5+7\right)x+\left(4-8\right)$

$=2{x}^{2}+12x-4$