Evaluate the following using suitable identities
$(999)^{3}$

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Solution

$(999)^{3} = (1000 - 1)^{3}$

$= (1000)^{3} - (1)^{3} - 3 (1000) (1) (1000 - 1)$ ......................... $(∵ (x - y)^{3} = x^{3} - y^{3} - 3 x y (x - y))$

$= 1000000000 - 1 - 3000 (999)$

$= 1000000000 - 1 - 2997000 = 997002999$

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