What is the result of combining the expression: 9xy^2 + 3xy - 2xy^2 + 4xy?

• A. 7xy^2 + 7xy
• B. 11xy^2 + 7xy
• C. 5xy + xy^2
• D. 7xy^2 + 6xy

Answer: (A)

To find the result of combining the like terms in the expression (9xy^2 + 3xy - 2xy^2 + 4xy), you first need to identify and group the like terms.

The terms (9xy^2) and (-2xy^2) are like terms because they both contain the variable (xy^2). When you combine these terms, you perform the operation (9xy^2 + (-2xy^2)), which calculates to (7xy^2).

Next, you should look at the coefficients of the terms that include (xy). The terms (3xy) and (4xy) are like terms as well. Adding these gives (3xy + 4xy), which simplifies to (7xy).

Putting it all together, after combining the like terms, you end up with the expression (7xy^2 + 7xy). This matches the correct answer, confirming that your calculation and understanding of combining like terms is accurate. This method of grouping and simplifying is essential in algebra, allowing for clearer and more manageable expressions.