Combine like terms: What is the result of 9xy - 2xy + 3z?

• A. 7xy + 3z
• B. 5xy + 3z
• C. 11xy + 3z
• D. 3z

Answer: (A)

To combine like terms effectively, it's important to identify which terms can be added or subtracted. In this case, the terms "9xy" and "-2xy" are like terms because they both contain the variable "xy."

To combine them, you perform the operation:

9xy - 2xy = (9 - 2)xy = 7xy.

The term "3z" is not like terms with "xy" because it involves a different variable ("z"), so it remains unchanged in the expression.

Now, we can combine the results. After adding the like terms, you have:

7xy + 3z.

This matches the first option, proving that the correct result of combining the like terms is 7xy + 3z. This approach clearly emphasizes the understanding that only terms with the same variable components can be combined, which is foundational in algebraic simplification.