If `p =102,` then the value of `p (p^(2) - 6p + 12)` is :

Options

A. 1000008
B. 10000008
C. 999992
D. 9999992

Answer

To solve the problem where \( p = 102 \) and we need to find the value of \( p (p^2 - 6p + 12) \), we can follow these steps:

### Step 1: Substitute the value of \( p \)
We start by substituting \( p = 102 \) into the expression \( p (p^2 - 6p + 12) \).

\[ p (p^2 - 6p + 12) = 102 (102^2 - 6 \times 102 + 12) \]

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

\[ 102^2 = 10404 \]

### Step 3: Calculate \( 6p \)
Now, we calculate \( 6p \):

\[ 6 \times 102 = 612 \]

### Step 4: Substitute back into the expression
Now we substitute \( p^2 \) and \( 6p \) back into the expression:

\[ p^2 - 6p + 12 = 10404 - 612 + 12 \]

### Step 5: Simplify the expression
Now, we simplify the expression:

\[ 10404 - 612 = 9762 \]
\[ 9762 + 12 = 9774 \]

### Step 6: Multiply by \( p \)
Now we multiply by \( p \):

\[ 102 \times 9774 \]

### Step 7: Calculate the final value
Now we perform the multiplication:

\[ 102 \times 9774 = 995148 \]

Thus, the final value of \( p (p^2 - 6p + 12) \) when \( p = 102 \) is:

\[ \boxed{995148} \]

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