# Combining ("Gathering") Like Terms

First, we'll define what "terms" are. Then we'll see what "like terms" are.

A term is a product of a number and some variables, like $3xy$ or $-4{x}^{2}$ . If the variable part is the same in two terms, they're called like terms .

Examples :

$3x$ and $5x$ are like terms; $3x$ and $5y$ are unlike terms.

$7{a}^{3}b$ and $99{a}^{3}b$ are like terms; $7ab$ and $99a{b}^{2}$ are unlike.

If two terms are "like" then you can add or subtract them. Notice the use of the Distributive Property here.

$3x+5x=\left(3+5\right)x=8x$

The variable part stays the same; we can just add the coefficients (the numbers in front of the variables).

But unlike terms can't be added.

$3x+4y\ne 7x$ or $7y$ or $7xy$ , and

$6+5x\ne 11x$ .

(The symbol $\ne$ means "not equal to.")

This is important when simplifying polynomials .

Example:

Simplify.

$6{x}^{2}+5x+4-4{x}^{2}+7x-8$

First, collect the like terms in parentheses.

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

Then simplify.

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