If a = 1 and b = (-3), the value of `4a^(3)b^(2) - 3a^(2)b + 4ab^(2) - ab ` is

Options

A. `-84`
B. 84
C. `-108`
D. `-72`

Answer

To find the value of the expression \(4a^3b^2 - 3a^2b + 4ab^2 - ab\) when \(a = 1\) and \(b = -3\), we will substitute these values into the expression step by step.

### Step-by-Step Solution:

1. **Substitute the values of \(a\) and \(b\)**:
\[ 4(1)^3(-3)^2 - 3(1)^2(-3) + 4(1)(-3)^2 - (1)(-3) \]

2. **Calculate \(1^3\) and \((-3)^2\)**:
\[ 1^3 = 1 \quad \text{and} \quad (-3)^2 = 9 \]
Substitute these values back into the expression:
\[ 4(1)(9) - 3(1)(-3) + 4(1)(9) - (1)(-3) \]

3. **Simplify each term**:
- The first term: \(4 \cdot 1 \cdot 9 = 36\)
- The second term: \(-3 \cdot 1 \cdot -3 = 9\) (note that multiplying two negatives gives a positive)
- The third term: \(4 \cdot 1 \cdot 9 = 36\)
- The fourth term: \(-1 \cdot -3 = 3\)

Now, substitute these results back into the expression:
\[ 36 + 9 + 36 + 3 \]

4. **Combine all the terms**:
\[ 36 + 9 = 45 \]
\[ 45 + 36 = 81 \]
\[ 81 + 3 = 84 \]

5. **Final Result**:
The value of the expression \(4a^3b^2 - 3a^2b + 4ab^2 - ab\) when \(a = 1\) and \(b = -3\) is \(84\).