Evaluate the following using suitable identities: (i) (99)3 (ii) (102)3 (iii) (998)3
Solution and Explanation
It is known that,
(a + b)3 = a3 + b3 + 3ab(a + b)
nd (a - b)3 = a3 - b3 - 3ab (a - b)
(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.
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