Question

Evaluate using algebraic formula:

99³

Answer 1

99³ =  (100 − 1)³

Let a = 100, b = 1

Using the identity,

(a ± b)³ = a³ ± 3a²b + 3ab² ± b³

(100 − 1)³ = (100)³ − 3(100)²(1) + 3(100)(1)² − (1)³

= 10,00000 − 3(10000) (1) + 3(100) (1) − 1

= 1000000 − 3(10000) + 3(100) − 1

= 1000000 − 30000 + 300 − 1

= 970000 + 299

∴ (100 − 1)³ = 970299

Hence, 99³ = 970299