Question

Evaluate the following using suitable identities:- (998)³ 

Answer 1

It is known that,

(a + b)³ = a³ + b³ + 3ab(a + b)      and       (a - b)³ = a³ - b³ - 3ab(a - b)

∴ (998)³ = (1000 − 2)³

             = (1000)³ − (2)³ − 3(1000)(2)(1000 − 2)

             = 1000000000 − 8 − 6000(998)

             = 1000000000 − 8 − 5988000

             = 1000000000 − 5988008

             = 994011992