Evaluate the following using suitable identities:
Evaluate the following using suitable identities:
(i) (99)3 (ii) (102)3 (iii) (998)3
Answer
(i) (99)3 = (100 - 1)3
Using identity, (a - b)3 = a3 - b3 - 3ab(a - b)
(100 - 1)3 = (100)3 - 13 - (3×100×1)(100 - 1)
= 1000000 - 1 - 300(100 - 1)
= 1000000 - 1 - 30000 + 300
= 970299
(ii) (102)3 = (100 + 2)3
Using identity, (a + b)3 = a3 + b3 + 3ab(a + b)
(100 + 2)3 = (100)3 + 23 + (3×100×2)(100 + 2)
= 1000000 + 8 + 600(100 + 2)
= 1000000 + 8 + 60000 + 1200
= 1061208
(iii) (998)3
Using identity, (a - b)3 = a3 - b3 - 3ab(a - b)
(1000 - 2)3 = (1000)3 - 23 - (3×1000×2)(1000 - 2)
= 100000000 - 8 - 6000(1000 - 2)
= 100000000 - 8- 600000 + 12000
= 994011992
