If `p = 99` then, the value of `p(p^(2) + 3p + 3)` is :

Options

A. 989898
B. 988899
C. 999999
D. 998889

Answer

To solve the expression \( p(p^2 + 3p + 3) \) given that \( p = 99 \), we will follow these steps:

### Step 1: Substitute the value of \( p \)
We start by substituting \( p = 99 \) into the expression.

\[ p(p^2 + 3p + 3) = 99(99^2 + 3 \cdot 99 + 3) \]

### Step 2: Calculate \( 99^2 \)
Next, we calculate \( 99^2 \).

\[ 99^2 = 9801 \]

### Step 3: Calculate \( 3 \cdot 99 \)
Now, we calculate \( 3 \cdot 99 \).

\[ 3 \cdot 99 = 297 \]

### Step 4: Substitute back into the expression
Now we substitute the values back into the expression.

\[ 99(9801 + 297 + 3) \]

### Step 5: Simplify inside the parentheses
Now, we simplify the expression inside the parentheses.

\[ 9801 + 297 + 3 = 10101 \]

### Step 6: Multiply by \( 99 \)
Finally, we multiply \( 99 \) by \( 10101 \).

\[ 99 \cdot 10101 = 999999 \]

Thus, the value of \( p(p^2 + 3p + 3) \) when \( p = 99 \) is:

\[ \boxed{999999} \]