If `p = 99` then the values of `p ( p ^(2) + 3p + 3)` is

Options

A. 1000000
B. 999000
C. 999999
D. 990000

Answer

To solve the expression \( p ( p^2 + 3p + 3) \) when \( p = 99 \), we can 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 \( p^2 \)
Next, we calculate \( 99^2 \):
\[ 99^2 = 9801 \]

### Step 3: Calculate \( 3p \)
Now, we calculate \( 3 \cdot 99 \):
\[ 3 \cdot 99 = 297 \]

### Step 4: Add the terms inside the parentheses
Now we can add \( 99^2 \), \( 3p \), and \( 3 \):
\[ 99^2 + 3p + 3 = 9801 + 297 + 3 = 10001 \]

### Step 5: Multiply by \( p \)
Now we multiply the result by \( p \):
\[ 99 \cdot 10001 = 990099 \]

### Final Answer
Thus, the value of \( p ( p^2 + 3p + 3) \) when \( p = 99 \) is:
\[ \boxed{990099} \]

---