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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,

6 x + 4 y − 2 x + 2

The four terms of the above expression are 6 x , 4 y , − 2 x and 2 .

Like Terms:

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

For example:

4 x + 18 y − 3 x − 7 x + 3 x y

In the above expression 4 x , − 3 x and − 7 x are like terms. 18 y and 3 x y 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 12 a + 3 b − 8 b − 8 a + a − 7 b .

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

( 12 a − 8 a + a ) + ( 3 b − 8 b − 7 b )

Use the Distributive Property to combine like terms.

( 12 − 8 + 1 ) a + ( 3 − 8 − 7 ) b

= 5 a − 12 b