# 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.

(12a – 8a + a) + (3b – 8b – 7b)

Use the Distributive Property to combine like terms.

(12 – 8 + 1 )a +(3 – 8 – 7 )b

= 5a – 12b