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

Options

A. `4x^(2)y^(2)`
B. `8xy^(2)-6y^(2)`
C. `2x^(2)y+2xy^(2)`
D. `2x^(2)y+8xy^(2)-6y^(2)`

Answer

To solve the expression \((x^{2}y - 3y^{2} + 5xy^{2}) - (-x^{2}y + 3xy^{2} - 3y^{2})\), we will follow these steps:

### Step 1: Distribute the negative sign
We start by distributing the negative sign across the second set of parentheses:
\[ (x^{2}y - 3y^{2} + 5xy^{2}) + (x^{2}y - 3xy^{2} + 3y^{2}) \]

### Step 2: Combine like terms
Now we will combine the like terms from the expression:
\[ x^{2}y + x^{2}y + (-3y^{2} + 3y^{2}) + (5xy^{2} - 3xy^{2}) \]

### Step 3: Simplify the expression
Now we simplify the expression:
- Combine \(x^{2}y + x^{2}y\) to get \(2x^{2}y\).
- The terms \(-3y^{2} + 3y^{2}\) cancel out to \(0\).
- Combine \(5xy^{2} - 3xy^{2}\) to get \(2xy^{2}\).

Putting it all together, we have:
\[ 2x^{2}y + 2xy^{2} \]

### Final Result
Thus, the simplified expression is:
\[ 2x^{2}y + 2xy^{2} \]