If a * b= `a^(2) + ab + b^(2)`, then find the value of 2 * 3?

Options

A. 6
B. 19
C. 82
D. 26

Answer

To solve the problem where \( a * b = a^2 + ab + b^2 \), we need to find the value of \( 2 * 3 \).

### Step 1: Substitute the values into the expression
We start by substituting \( a = 2 \) and \( b = 3 \) into the expression \( a * b \).

\[ 2 * 3 = 2^2 + (2 \cdot 3) + 3^2 \]

### Step 2: Calculate \( 2^2 \)
Now, we calculate \( 2^2 \):

\[ 2^2 = 4 \]

### Step 3: Calculate \( 2 \cdot 3 \)
Next, we calculate \( 2 \cdot 3 \):

\[ 2 \cdot 3 = 6 \]

### Step 4: Calculate \( 3^2 \)
Now, we calculate \( 3^2 \):

\[ 3^2 = 9 \]

### Step 5: Add the results together
Now we add all the results from the previous steps:

\[ 2 * 3 = 4 + 6 + 9 \]

### Step 6: Final calculation
Now, we perform the final addition:

\[ 4 + 6 = 10 \]
\[ 10 + 9 = 19 \]

Thus, the value of \( 2 * 3 \) is \( 19 \).

### Final Answer:
\[ 2 * 3 = 19 \]