`x^(**) y = (x + 1)^2 . (y-2)` then what is the value of 6*5 ?

Options

A. 147
B. 192
C. 105
D. 182

Answer

To solve the equation \( x \cdot y = (x + 1)^2 \cdot (y - 2) \) and find the value of \( 6 \cdot 5 \), we can follow these steps:

### Step 1: Substitute \( x = 6 \) and \( y = 5 \) into the equation.
We start by substituting the values of \( x \) and \( y \) into the given equation.

\[ x \cdot y = 6 \cdot 5 \]

### Step 2: Calculate \( x \cdot y \).
Now we calculate \( 6 \cdot 5 \).

\[ 6 \cdot 5 = 30 \]

### Step 3: Substitute into the right side of the equation.
Next, we substitute \( x = 6 \) and \( y = 5 \) into the right side of the equation \( (x + 1)^2 \cdot (y - 2) \).

\[ (6 + 1)^2 \cdot (5 - 2) \]

### Step 4: Simplify the expression.
Now we simplify the expression:

\[ (7)^2 \cdot (3) \]

### Step 5: Calculate \( 7^2 \) and then multiply by 3.
Calculating \( 7^2 \):

\[ 7^2 = 49 \]

Now multiply by 3:

\[ 49 \cdot 3 = 147 \]

### Conclusion:
Thus, the value of \( 6 \cdot 5 \) according to the equation is:

\[ \boxed{147} \]