Q. 214.2( 12 Votes )

Evaluate, using iden

Answer :

(i) 1023 = (100 + 2)3
          = (100)3 + 3(100)2 (2) + 3(100)(22) + 23     [ by using (a + b)3 = a3 + b3 +3a2b +3ab2]
          = 10, 00, 000 + 60, 000 + 1200 + 8  
           = 10, 61, 208
(ii) 993 = (100 - 1)                                                         [ by using (a - b)3 = a3 - b-3a2b + 3ab2]
          = 1003 - 3(100)2(1) + 3(100)(12) - 13
          = 10, 00, 000 - 30, 000 + 300 - 1
          =  9, 70, 299

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