If `a**b =2a - 3b + ab , ` then `3**5 + 5** 3 ` is equal to :

Options

A. 22
B. 24
C. 26
D. 28

Answer

To solve the problem where \( a \star b = 2a - 3b + ab \), we need to calculate \( 3 \star 5 + 5 \star 3 \).

### Step 1: Calculate \( 3 \star 5 \)
Using the definition of the operation \( a \star b \):
\[ 3 \star 5 = 2(3) - 3(5) + (3)(5) \]
Calculating each term:
- \( 2(3) = 6 \)
- \( -3(5) = -15 \)
- \( (3)(5) = 15 \)

Now substituting these values into the equation:
\[ 3 \star 5 = 6 - 15 + 15 \]
Simplifying:
\[ 3 \star 5 = 6 - 15 + 15 = 6 \]

### Step 2: Calculate \( 5 \star 3 \)
Now we calculate \( 5 \star 3 \) using the same operation:
\[ 5 \star 3 = 2(5) - 3(3) + (5)(3) \]
Calculating each term:
- \( 2(5) = 10 \)
- \( -3(3) = -9 \)
- \( (5)(3) = 15 \)

Now substituting these values into the equation:
\[ 5 \star 3 = 10 - 9 + 15 \]
Simplifying:
\[ 5 \star 3 = 10 - 9 + 15 = 16 \]

### Step 3: Combine the results
Now we combine the results of \( 3 \star 5 \) and \( 5 \star 3 \):
\[ 3 \star 5 + 5 \star 3 = 6 + 16 = 22 \]

### Final Answer
Thus, the value of \( 3 \star 5 + 5 \star 3 \) is \( \boxed{22} \).

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