#### Terms

A term is the product of a number and one or more variables. A term may also be a single number, with no variable.

The expression 14 + 3*y*^{2} - 15*zp* has three terms: 14, 3*y*^{2}, and -15*zp*.

The expression 7*z* + 12 + 2 + *z* has four terms: 7*z*, 12, 2, *z*.

The coefficient is the number that is multiplied by the variable(s) in a single term. In the expression 14 + 3*y*^{2} - 15*zp*, *y*^{2} has a coefficient of 3 and *zp* has a coefficient of -15. A term with no coefficient, like *z*, has an implied coef ficient of 1.

Terms that do not contain variables are called constants. In the above expressions, 14, 12, and 2 are constants.

#### Combining Like Terms

Like terms are terms that contain the exact same variables raised to the same exponents. For example, 15*yz* and 22*yz* are like terms, but 15*yz*^{2} and 22*yz* are not. Likewise, 12*w*^{2}*yz* and -5*w*^{2}*yz* are like terms, but 12*w*^{2}*yz* and -5*w*^{2}*z* are not. 12 and -6 are like terms, because they are both constant terms.

To combine like terms, group them together in the equation, putting the terms with the highest exponents on the left. We can do this because addition *commutes.* Next, group the coefficients of like terms together , all multiplied by the variable(s) in those terms. Finally, add the coefficients of the like terms (or subtract them if they are negative). Here are some examples:

*Example 1*: Simplify 4*y* + 15 - 2*y* + 5*y*^{2} + 12 - 6.

- 5
*y*^{2} + 4*y* - 2*y* + 15 + 12 - 6 (note that this expression and the original expression both contain 6 terms) - 5
*y*^{2} + (4 - 2)*y* + (15 + 12 - 6) - 5
*y*^{2} + 2*y* + 21

*Example 2*: Simplify

11*wz* + 6*w*^{2} -10*wz* + *wz* - 6 - 2*w* + 3*w*^{2}.

- 6
*w*^{2} +3*w*^{2} + 11*wz* - 10*wz* + *wz* - 2*w* - 6 (note that this expression and the original expression both contain 7 terms) - (6 + 3)
*w*^{2} + (11 - 10 + 1)*wz* - 2*w* - 6 - 9
*w*^{2} + 2*wz* - 2*w* - 6

*Example 3*: Simplify

-12*w*^{2} +6*w* - 7*w*^{3} +4*w*^{2} +8*w*^{2} - 2*w* + 5 + 9*w*.

- -7
*w*^{3} -12*w*^{2} +4*w*^{2} +8*w*^{2} + 6*w* - 2*w* + 9*w* + 5 (8 terms) - -7
*w*^{3} + (- 12 + 4 + 8)*w*^{2} + (6 - 2 + 9)*w* + 5 - -7
*w*^{3} +0*w*^{2} +13*w* + 5 = - 7*w*^{3} + 13*w* + 5

When we combine like terms, we convert the expression to simplified form. The expression is simplified form is equivalent to the original expression.