Are 2ab and 3a^2b like terms?

• A. Yes, they have the same variables
• B. No, they are not like terms
• C. Yes, same coefficients
• D. No, they differ in both variables and powers

Answer: (B)

To determine whether 2ab and 3a^2b are like terms, we need to analyze both the variables and their powers in each term. Like terms are defined as terms that have exactly the same variable factors, raised to the same powers.

In this case, the first term, 2ab, consists of the variable "a" raised to the first power and the variable "b" raised to the first power. The second term, 3a^2b, has "a" raised to the second power and "b" raised to the first power.

Since the powers of "a" differ between the two terms (first power in the first term versus second power in the second term), they cannot be combined as like terms. Furthermore, while both terms share the variable "b" at the first power, the different powers of "a" mean that they do not meet the requirements to be classified as like terms.

The correct choice indicates that they are not like terms because they differ in their powers, specifically concerning the variable "a".