Like Terms

Our Algebra 1 tutorial software program contains over 60 topic areas. One of them is Like Terms, and this page summarizes the main ideas of this topic. This page is intended for review, and is not a substitute for the interactive, self-paced tutorials of the MathTutor algebra 1 software program.

General Explanation

A TERM has two parts: the constant part and the variable part:
constant → 4x ← variable

LIKE TERMS are terms having the same variable part. In determining like terms, the constant part can be ignored. For example, 12y and -16y are like terms because the variable part ("y") is the same in both terms. 2x3 and 12x3 are also like terms.
CONSTANTS such as 14 and 2.3 are always considered like terms. Constants do not contain a variable part.
3xy2 and 5x2y are not like terms. Both terms have x and y, but the variable parts are not exactly the same. The variable parts must be the same to be like terms.

Sample Problem 1

Locate all the like terms in the following expression:
16 - 4 + 10 + 36xr - 82yr


All of the constants (16, -4, 10) are like terms. Since the last two terms have different variable parts, they are not like terms.

Sample Problem 2

Locate all of the like terms in the following expression:
21aw - 16y + 41z - 7au + 5z


41z and 5z are like terms, since they both contain the same variable part, "z". There are no other like terms.