Find the sum of the expresson
`- 15 a ^(2) + 3 ab - 6b ^(2)`
`a ^(2) - 5 ab + 11 b ^(2) , - 7a ^(2)- 18 ab - 13 b ^(2) and 26 a ^(2) - 16 ab - 7b ^(2).`

Options

A. `5 a ^(2) - 36 ab - 15 b ^(2) `
B. `5a ^(2) + 36 a b - 15 b ^(2)`
C. `5a ^(2) - 36 ab + 15 b ^(2)`
D. None of the above

Answer

To find the sum of the expressions:

1. **Expressions to sum**:
\[ -15a^2 + 3ab - 6b^2 \]
\[ + a^2 - 5ab + 11b^2 \]
\[ - 7a^2 - 18ab - 13b^2 \]
\[ + 26a^2 - 16ab - 7b^2 \]

2. **Combine all expressions**:
\[ (-15a^2 + 3ab - 6b^2) + (a^2 - 5ab + 11b^2) + (-7a^2 - 18ab - 13b^2) + (26a^2 - 16ab - 7b^2) \]

3. **Rearranging and grouping like terms**:
- Group \(a^2\) terms:
\[ -15a^2 + a^2 - 7a^2 + 26a^2 \]
- Group \(ab\) terms:
\[ 3ab - 5ab - 18ab - 16ab \]
- Group \(b^2\) terms:
\[ -6b^2 + 11b^2 - 13b^2 - 7b^2 \]

4. **Calculating the sum of \(a^2\) terms**:
\[ -15 + 1 - 7 + 26 = -15 - 7 + 1 + 26 = -22 + 27 = 5 \]
So, the coefficient of \(a^2\) is \(5\).

5. **Calculating the sum of \(ab\) terms**:
\[ 3 - 5 - 18 - 16 = 3 - 5 = -2, \quad -2 - 18 = -20, \quad -20 - 16 = -36 \]
So, the coefficient of \(ab\) is \(-36\).

6. **Calculating the sum of \(b^2\) terms**:
\[ -6 + 11 - 13 - 7 = -6 + 11 = 5, \quad 5 - 13 = -8, \quad -8 - 7 = -15 \]
So, the coefficient of \(b^2\) is \(-15\).

7. **Final expression**:
Combining all the results, we get:
\[ 5a^2 - 36ab - 15b^2 \]

### Final Answer:
\[ 5a^2 - 36ab - 15b^2 \]