Simplify : `4s^(2)t - 5st^(2) - 7s^(2)t - 3s^(2)t^(2) + 3st^(2) + 3s^(2)t - (-2st^(2))`

Options

A. 0
B. `-3st^(2)`
C. `3s^(2)t`
D. `-3s^(2)t^(2)`

Answer

To simplify the expression \(4s^2t - 5st^2 - 7s^2t - 3s^2t^2 + 3st^2 + 3s^2t - (-2st^2)\), we will follow these steps:

### Step 1: Rewrite the expression
We start with the expression:
\[ 4s^2t - 5st^2 - 7s^2t - 3s^2t^2 + 3st^2 + 3s^2t - (-2st^2) \]
We can rewrite \(- (-2st^2)\) as \(+ 2st^2\):
\[ 4s^2t - 5st^2 - 7s^2t - 3s^2t^2 + 3st^2 + 3s^2t + 2st^2 \]

### Step 2: Group like terms
Next, we group the like terms together:
- Terms with \(s^2t\): \(4s^2t - 7s^2t + 3s^2t\)
- Terms with \(st^2\): \(-5st^2 + 3st^2 + 2st^2\)
- Terms with \(s^2t^2\): \(-3s^2t^2\)

### Step 3: Simplify each group
Now, we simplify each group:
1. For \(s^2t\):
\[ 4s^2t - 7s^2t + 3s^2t = (4 - 7 + 3)s^2t = 0s^2t = 0 \]

2. For \(st^2\):
\[ -5st^2 + 3st^2 + 2st^2 = (-5 + 3 + 2)st^2 = 0st^2 = 0 \]

3. For \(s^2t^2\):
\[ -3s^2t^2 = -3s^2t^2 \]

### Step 4: Combine the results
Now, we combine the results from the simplification:
\[ 0 + 0 - 3s^2t^2 = -3s^2t^2 \]

### Final Answer
Thus, the simplified expression is:
\[ \boxed{-3s^2t^2} \]