For P = 99, evaluate the expression: P * (P^2 + 3P + 3) What is the exact value?

Introduction / Context:
This is an algebraic simplification and substitution problem. You substitute P = 99, compute P^2, evaluate the bracket, and then multiply. It also connects to the identity for (P + 1)^3 - 1, which often creates repeating 9 patterns.

Given Data / Assumptions:

• P = 99
• Expression: P * (P^2 + 3P + 3)

Concept / Approach:
Direct substitution works. Compute inside the parentheses first, then multiply by P. Keep arithmetic systematic to avoid mistakes with large numbers.

Step-by-Step Solution:

Verification / Alternative check:
Notice that (P + 1)^3 = P^3 + 3P^2 + 3P + 1, so (P^3 + 3P^2 + 3P) = (P + 1)^3 - 1. Here P*(P^2 + 3P + 3) = P^3 + 3P^2 + 3P, which equals (P + 1)^3 - 1. With P = 99, (100)^3 - 1 = 1,000,000 - 1 = 999,999.

Why Other Options Are Wrong:

Common Pitfalls:
Miscomputing 99^2, forgetting the +3 term, or doing 10101*99 as 10101*100 + 10101 instead of subtracting 10101.

Final Answer:
999999