Question

Evaluate (99)³ by using suitable identity.

Answer 1

Here, (99)³ = (100 − 1)³.
So, using the identity (a − b)³ = a³ − b³ − 3ab(a − b), we get
(99)³ = (100)³ − 1³ − 3(100)(1)(100 − 1)
= 1000000 − 1 − 300(99)
= 1000000 − 1 − 29700
= 1000000 − 29701
= 970299
Hence, (99)³ = 970299.