InterviewSolution
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InterviewSolution
| 1. |
Evaluate the following by using identities:(i) 983 (ii) 10013 |
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Answer» (i) 983 = (100 – 2)3 (a – b)3 ≡ a3 – 3a2b + 3ab2 – b3 983 = (100 – 2)3 = 1003 – 3 x 1002 x + 3 x 100 x 22 – 23 = 1000000 – 3 x 10000 x 2 + 300 x 4 – 8 = 1000000 – 60000 + 1200 – 8 = 1001200 – 60008 = 941192 (ii) 10013 = (1000 + 1)3 (a + b)3 ≡ a3 + 3a2b + 3ab2 + b3 (1000 + 1)3 = 10003 + 3(10002) x 1 + 3 x 1000 x 12 + 13 = 1000,000,000 + 3,000,000 + 3000 + 1 = 1,003,003,001 |
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