Like Terms

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.

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.

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.