(i) (99)3 = (100 – 1)3
As per Identity,
(a – b)3 = a3 – b3 – 3ab(a – b)
(100 – 1)3 = (100)3 – (1)3 – 3(100)(1)(100- 1)
(99)3 = 1000000 – 1 – 300(100 – 1)
= 1000000 – 1 – 30000 + 300 = 970299
∴ (99)3 = 970299
(ii) (102)3 = (100 + 2)3
As per Identity,
(a + b)3 = a3 + b3 + 3ab(a + b)
(100 + 2)3 = (100)3 + (2)3 + 3( 100)(2)( 100 + 2)
= 1000000 + 8 + 600( 100 + 2)
= 1000000 + 8 + 60000 + 1200 (100 + 2)3
= 1061208
∴ (102)3= 1061208
(iii) (998)3 = (1000 – 2)3
As per Identity,
(a – b)3 = a3 – b3 – 3ab(a – b)
(1000 – 2)3 = (1000)3 – (2)3 – 3( 1000) (2)(1000 – 2)
= 1000000000 – 8 – 6000(1000 – 1)
= 1000000000 – 8 – 6000000 + 6000
= 994005992
∴ (998)3 = 994005992