Subtract the second polynomial from the first :
`3x^(2)y-7xy^(2) +5xy, 2xy-x^(2)y +7xy^(2)`

Answer

To subtract the second polynomial from the first, we will follow these steps:

### Step 1: Write down the polynomials
The first polynomial is:
\[ P_1 = 3x^2y - 7xy^2 + 5xy \]

The second polynomial is:
\[ P_2 = 2xy - x^2y + 7xy^2 \]

### Step 2: Set up the subtraction
We need to subtract \( P_2 \) from \( P_1 \):
\[ P_1 - P_2 = (3x^2y - 7xy^2 + 5xy) - (2xy - x^2y + 7xy^2) \]

### Step 3: Distribute the negative sign
Distributing the negative sign to the second polynomial gives us:
\[ P_1 - P_2 = 3x^2y - 7xy^2 + 5xy - 2xy + x^2y - 7xy^2 \]

### Step 4: Combine like terms
Now, we will combine the like terms:

1. **For \( x^2y \)** terms:
\[ 3x^2y + x^2y = (3 + 1)x^2y = 4x^2y \]

2. **For \( xy^2 \)** terms:
\[ -7xy^2 - 7xy^2 = -14xy^2 \]

3. **For \( xy \)** terms:
\[ 5xy - 2xy = (5 - 2)xy = 3xy \]

### Step 5: Write the final result
Combining all the results from above, we get:
\[ P_1 - P_2 = 4x^2y - 14xy^2 + 3xy \]

### Final Answer
Thus, the final answer is:
\[ 4x^2y - 14xy^2 + 3xy \]

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