Example 23 - Evaluate each of the following using suitable - Identity VI & VII

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Example 23 Evaluate each of the following using suitable identities: (104)3 We write 104= 100 + 4 (104)3 = (100 + 4)3 Using (a + b)3 = a3 + b3 + 3ab(a + b) Where a = 100 & b = 4 = (100)3 + (4) 3 + 3(100)(4)(100 + 4) = 1000000 + 64 + 3(100)(4)(104) = 1000000 + 64 + 124800 = 1124864 Example 23 Evaluate each of the following using suitable identities: (ii) (999) 3 We write 999 = 1000 – 1 (999) 3 = (1000 – 1) 3 Using (a – b)3 = a3 – b3 – 3ab(a – b) Where a = 1000 & b = 1 = (1000) 3 – (1) 3 – 3(1000)(1)(1000 – 1) = 1000000000 – 1 – 3(1000)(1)(999) = 1000000000 – 1 – 2997000 = 997002999

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