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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 + 2 x y 9 x + 2

The four terms of the above expression are 3 x 2 y , 2 x y , 9 x and 2 .

Like Terms:

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

For Example,

7 x 3 14 x 2 8 x 3 x 3 + 9

In the above expression 7 x 3 , and 3 x 3 are like terms. 14 x 2 , 8 x 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 + 5 x + 4 4 x 2 + 7 x 8

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

( 6 x 2 4 x 2 ) + ( 5 x + 7 x ) + ( 4 8 )

Use the Distributive Property to combine like terms.

( 6 4 ) x 2 + ( 5 + 7 ) x + ( 4 8 )

= 2 x 2 + 12 x 4