# 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,

3x2y + 2xy – 9x + 2

The four terms of the above expression are 3x2y, 2xy, –9x and 2.

Like Terms:

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

For Example,

7x3 – 14x2 – 8x – 3x3 + 9

In the above expression 7x3, and –3x3 are like terms. –14x2 , – 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 6x2 + 5x + 4 – 4x2 + 7x – 8

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

(6x2– 4x2) + (5x + 7x) + (4 – 8)

Use the Distributive Property to combine like terms.

(6 – 4)x2 + (5 + 7)x + (4 – 8)

= 2x2 + 12x – 4