How much bigger is `5x^(2)y^(2) - 18xy^(2) - 10x^(2)y` than `-5x^(2) + 6x^(2)y - 7xy` ?

Answer

To find out how much bigger the polynomial \(5x^2y^2 - 18xy^2 - 10x^2y\) is than the polynomial \(-5x^2 + 6x^2y - 7xy\), we need to calculate the difference between the two polynomials.

### Step-by-Step Solution:

1. **Identify the Polynomials**:
- First polynomial: \(P_1 = 5x^2y^2 - 18xy^2 - 10x^2y\)
- Second polynomial: \(P_2 = -5x^2 + 6x^2y - 7xy\)

2. **Set Up the Difference**:
To find how much bigger \(P_1\) is than \(P_2\), we calculate:
\[ \text{Difference} = P_1 - P_2 \]

3. **Substitute the Polynomials**:
\[ \text{Difference} = (5x^2y^2 - 18xy^2 - 10x^2y) - (-5x^2 + 6x^2y - 7xy) \]

4. **Remove the Parentheses**:
When we subtract \(P_2\), we need to distribute the negative sign:
\[ \text{Difference} = 5x^2y^2 - 18xy^2 - 10x^2y + 5x^2 - 6x^2y + 7xy \]

5. **Combine Like Terms**:
Now, we will combine the like terms:
- For \(x^2y^2\): \(5x^2y^2\)
- For \(xy^2\): \(-18xy^2\)
- For \(x^2y\): \(-10x^2y - 6x^2y = -16x^2y\)
- For \(x^2\): \(5x^2\)
- For \(xy\): \(7xy\)

Thus, we have:
\[ \text{Difference} = 5x^2y^2 - 18xy^2 - 16x^2y + 5x^2 + 7xy \]

6. **Final Expression**:
The final expression for the difference is:
\[ \text{Difference} = 5x^2y^2 - 18xy^2 - 16x^2y + 5x^2 + 7xy \]

### Conclusion:
The first polynomial \(5x^2y^2 - 18xy^2 - 10x^2y\) is represented by the expression \(5x^2y^2 - 18xy^2 - 16x^2y + 5x^2 + 7xy\) which shows how much bigger it is than the second polynomial.