Question

Evaluate the following using suitable identities:

(i) (99)³ (ii) (102)³ (iii) (998)³

Answer 1

It is known that,

(i) (99)³ = (100 − 1)³

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

= 1000000 − 1 − 300(99)

= 1000000 − 1 − 29700

= 970299

(ii) (102)³ = (100 + 2)³

= (100)³ + (2)³ + 3(100) (2) (100 + 2)

= 1000000 + 8 + 600 (102)

= 1000000 + 8 + 61200

= 1061208

(iii) (998)³= (1000 − 2)³

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

= 1000000000 − 8 − 6000(998)

= 1000000000 − 8 − 5988000

= 1000000000 − 5988008

= 994011992