If `a *** b = 2 a + 3b - ab` , then the value of `(3 *** 5 + 5 *** 3)` is

Options

A. 10
B. 6
C. 4
D. 2

Answer

To solve the problem, we need to evaluate the expression \( (3 *** 5 + 5 *** 3) \) using the operation defined as \( a *** b = 2a + 3b - ab \).

### Step-by-step Solution:

1. **Calculate \( 3 *** 5 \)**:
- Substitute \( a = 3 \) and \( b = 5 \) into the operation:
\[ 3 *** 5 = 2(3) + 3(5) - (3)(5) \]
- Calculate each term:
- \( 2(3) = 6 \)
- \( 3(5) = 15 \)
- \( (3)(5) = 15 \)
- Now substitute these values back into the equation:
\[ 3 *** 5 = 6 + 15 - 15 \]
- Simplify:
\[ 3 *** 5 = 6 + 0 = 6 \]

2. **Calculate \( 5 *** 3 \)**:
- Substitute \( a = 5 \) and \( b = 3 \) into the operation:
\[ 5 *** 3 = 2(5) + 3(3) - (5)(3) \]
- Calculate each term:
- \( 2(5) = 10 \)
- \( 3(3) = 9 \)
- \( (5)(3) = 15 \)
- Now substitute these values back into the equation:
\[ 5 *** 3 = 10 + 9 - 15 \]
- Simplify:
\[ 5 *** 3 = 19 - 15 = 4 \]

3. **Combine the results**:
- Now we need to add the results of \( 3 *** 5 \) and \( 5 *** 3 \):
\[ 3 *** 5 + 5 *** 3 = 6 + 4 \]
- Simplify:
\[ 3 *** 5 + 5 *** 3 = 10 \]

### Final Answer:
The value of \( (3 *** 5 + 5 *** 3) \) is \( \boxed{10} \).