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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.

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

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