Can you combine the terms 3x^2y and 6xy^2? Why or why not?

• A. Yes, they have the same coefficient
• B. No, they are not like terms
• C. Yes, they can be summed directly
• D. No, they have different powers

Answer: (B)

You cannot combine the terms 3x^2y and 6xy^2 because they are not like terms. Like terms are those that have the same variable parts raised to the same powers. In this situation, 3x^2y contains the variable x raised to the second power, while 6xy^2 has x raised to the first power. Additionally, the variable y appears as y to the first power in the first term and y squared in the second term. Since the powers of the variables differ, these terms cannot be combined through addition or subtraction.

The other aspects mentioned in the incorrect answers do not accurately address why the terms cannot be combined. While coefficients may play a role in combining like terms, they must share the same variable factors raised to identical powers to be combined.