Evaluate
(i) $(103)^{3}$ (ii) $(99)^{3}$

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Solution

(i) $103^{3} = (100 + 3)^{3} = 100^{3} + 3^{3} + 3 \times 100 \times 3 (100 + 3) = 1000000 + 27 + 900 \times 103 = 1000000 + 27 + 92700 = 1092727$

(ii) $99^{3} = (100 - 1)^{3} = 100^{3} - 1^{3} - 3 \times 100 \times 1 (100 - 1) = 1000000 - 1 - 300 \times 99 = 1000000 - 1 - 29700 = 970299$

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