Using suitable identity, evaluate the following:
(i) 1033
(ii) 101 × 102
(iii) 9992
(i) (103)3
Given that: (103)3
= (100 + 3)3
= (100)3 + (3)3 + 3(100)23 + 3(100)32
[∵ (a + b)3 = (a3 + b3 + 3a2 b + 3ab2)]
= 1000000 + 27 + 90000 + 2700
= 1092727
(ii). Given that: 101 × 102
= (100 + 1) × (100 + 2)
= (100)2 + (1 + 2)100 + 1 × 2
[∵ (