By using suitable identities, evaluate the following:
(i) (103)3
(ii) (99)3
(iii) (10.1)3
Answer :
(i) (103)3
It can be written as
= (100 + 3)3
Expanding using formula
= 1003 + 33 + 3 × 100 × 3 (100 + 3)
By further calculation
= 1000000 + 27 + 900 × 103
So we get
= 1000000 + 27 + 92700
= 1092727
(ii) (99)3
It can be written as
= (100 – 1)3
Expanding using formula
= 1003 – 13 – 3 × 100 × 1 (100 – 1)
By further calculation
= 1000000 – 1 – 300 × 99
So we get
= 1000000 – 1 – 29700
= 1000000 – 29701
= 970299
(iii) (10.1)3
It can be written as
= (10 + 0.1)3
Expanding using formula
= 103 + 0.13 + 3 × 10 × 0.1 (10 + 0.1)
By further calculation
= 1000 + 0.001 + 3 × 10.1
So we get
= 1000 + 0.001 + 30.3
= 1030.301
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