Question

Evaluate the following using suitable identities:

(99)³

Answer 1

It is known that,

(a + b)³ = a³ + b³ + 3ab(a + b)

and (a- b)³ = a³ - b³ -3ab(a - b)

 (99)³ = (100 − 1)³

= (100)³ − (1)³ − 3(100) (1) (100 − 1)

= 1000000 − 1 − 300(99)

= 1000000 − 1 − 29700

= 970299