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Let's work through this problem step by step.

We are given the expression:

\[
(x^2y - 3y^2 + 5xy^2) - (-x^2y + 3xy^2 - 3y^2)
\]

First, we distribute the negative sign across the second set of parentheses:

\[
= (x^2y - 3y^2 + 5xy^2) + (x^2y - 3xy^2 + 3y^2)
\]

Now, let's group the like terms together:

1. For \(x^2y\): \(x^2y + x^2y = 2x^2y\)
2. For \(y^2\): \(-3y^2 + 3y^2 = 0\) (these cancel out)
3. For \(xy^2\): \(5xy^2 - 3xy^2 = 2xy^2\)

Now, combining all of these:

\[
2x^2y + 2xy^2
\]

This matches option **C**: \(2x^2y + 2xy^2\).

### Final Answer: C

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Do you want more details on any step, or do you have any questions?

Here are 5 related questions to consider:
1. How would the solution change if the signs inside the parentheses were different?
2. What is the process for distributing negative signs in more complex expressions?
3. How do you recognize and combine like terms in algebraic expressions?
4. Could this type of problem involve factoring instead of combining like terms?
5. How would the answer change if one term were squared instead of linear?

**Tip:** Always double-check signs when distributing negative terms across an expression. Misplacing a negative can lead to the wrong final result!

Which of the following is equivalent to the expression (x^2y - 3y^2 + 5xy^2) - (-x^2y + 3xy^2 - 3y^2)?

Learn how to simplify the expression (x^2y - 3y^2 + 5xy^2) - (-x^2y + 3xy^2 - 3y^2) using the distributive property and combining like terms. This problem involves algebraic manipulation suitable for students in Grades 8-10.

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