Subtract :
`5x^(2)-3xy -7y^(2)` from `3x^(2)-xy-2y^(2)`

Answer

To solve the problem of subtracting the expression \(5x^2 - 3xy - 7y^2\) from \(3x^2 - xy - 2y^2\), we can follow these steps:

### Step-by-Step Solution:

1. **Write the expressions clearly**:
We need to subtract the expression \(5x^2 - 3xy - 7y^2\) from \(3x^2 - xy - 2y^2\). This can be written as:
\[ (3x^2 - xy - 2y^2) - (5x^2 - 3xy - 7y^2) \]

2. **Distribute the negative sign**:
When we subtract the second expression, we need to distribute the negative sign across all terms in the second expression:
\[ 3x^2 - xy - 2y^2 - 5x^2 + 3xy + 7y^2 \]

3. **Combine like terms**:
Now, we will combine the like terms:
- For \(x^2\) terms: \(3x^2 - 5x^2 = -2x^2\)
- For \(xy\) terms: \(-xy + 3xy = 2xy\)
- For \(y^2\) terms: \(-2y^2 + 7y^2 = 5y^2\)

Putting it all together, we have:
\[ -2x^2 + 2xy + 5y^2 \]

4. **Final answer**:
Thus, the result of the subtraction is:
\[ -2x^2 + 2xy + 5y^2 \]