Like Terms
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. 2x^{3} and 12x^{3} are also like terms. CONSTANTS such as 14 and 2.3 are always considered like terms. Constants do not contain a variable part. 3xy^{2} and 5x^{2}y 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 Solution
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 Solution
41z and 5z are like terms, since they both contain the same variable part, "z". There are no
other like terms.
