Evaluate the following using suitable identities.
$(99)^{3}$

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Solution

$(99)^{3} = (100 - 1)^{3}$
Suitable identities is $(x - y)^{3} = x^{3} - 3 x^{2} y + 3 x y^{2} - y^{3}$
$∴ (100 - 1)^{3}$
$= (100)^{3} - 3 (100)^{2} (1) + 3 (100) (1)^{2} - (1)^{3}$
$= 1000000 - 30000 + 300 - 1 = 970299$

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