If a term is 8xy, which of the following is NOT a like term?

• A. 2xy
• B. 8x
• C. -4xy
• D. 5xy

Answer: (B)

To determine which term is not a like term with 8xy, we need to understand what constitutes like terms. Like terms are terms that contain the same variables raised to the same powers, allowing us to combine them through addition or subtraction.

The term 8xy consists of the variables x and y, both raised to the first power. Now, let’s analyze the choices:

• The term 2xy has the same variables, x and y, both multiplied together and each raised to the first power. Therefore, it is a like term.

• The term -4xy also contains the same variables x and y raised to the same powers as in 8xy, making it another like term.

• The term 5xy is similarly constructed, with both variables included in the same way as 8xy. It is also a like term for the same reasons.

On the other hand, the term 8x only includes the variable x, missing y entirely. Since it does not share both variables with the same powers as 8xy, it is not considered a like term. This distinction makes it the only option that does not fit the criteria for like terms with 8xy.