Find the value of `(25 a ^(2) + 16 b ^(2) + 9 + 40 ab - 2 4b - 30 a)` at `a =- 1` and `b =2.`

Answer

To find the value of the expression \( 25a^2 + 16b^2 + 9 + 40ab - 24b - 30a \) at \( a = -1 \) and \( b = 2 \), we will substitute the values of \( a \) and \( b \) into the expression and simplify step by step.

### Step-by-Step Solution:

1. **Substituting the values**:
Substitute \( a = -1 \) and \( b = 2 \) into the expression:
\[ 25(-1)^2 + 16(2)^2 + 9 + 40(-1)(2) - 24(2) - 30(-1) \]

2. **Calculating each term**:
- Calculate \( 25(-1)^2 \):
\[ 25 \times 1 = 25 \]
- Calculate \( 16(2)^2 \):
\[ 16 \times 4 = 64 \]
- The constant term is \( 9 \).
- Calculate \( 40(-1)(2) \):
\[ 40 \times -1 \times 2 = -80 \]
- Calculate \( -24(2) \):
\[ -24 \times 2 = -48 \]
- Calculate \( -30(-1) \):
\[ -30 \times -1 = 30 \]

3. **Combining all terms**:
Now, combine all the calculated values:
\[ 25 + 64 + 9 - 80 - 48 + 30 \]

4. **Simplifying the expression**:
- First, combine the positive terms:
\[ 25 + 64 + 9 + 30 = 128 \]
- Now combine the negative terms:
\[ -80 - 48 = -128 \]
- Finally, combine the results:
\[ 128 - 128 = 0 \]

### Final Answer:
The value of the expression at \( a = -1 \) and \( b = 2 \) is \( 0 \).