Question

Evaluate using algebraic formula:

99³ + 3(99)² + 3(99) + 1

Answer 1

99³ + 3(99)² + 3(99) + 1

This expression matches with,

(a + 1)³ = a³ + 3a² + 3a + 1   ...[Using (a + b)³ = a³ + 3a²b + 3ab² + b³]

Here, in the expression b = 1,

Thus, 

(99 + 1)³ = 99³ + 3(99)² + 3(99) + 1

∴ (99 + 1)³ = (100)³

= 100 × 100 × 100

∴ (99 + 1)³ = 1000000

Hence, using an algebraic formula for 99³ + 3(99)² + 3(99) + 1, we get 1000000.