Evaluate the following using suitable identities.
$(998)^{3}$

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Solution

$(998)^{3} = (1000 - 2)^{3}$
Suitable identities is $(x - y)^{3} = x^{3} - 3 x^{2} y + 3 x y^{2} - y^{3}$
$∴ (1000 - 2)^{3}$
$= (1000)^{3} - 3 (1000)^{2} (2) + 3 (1000) (2)^{2} - (2)^{3}$
$= 1000000000 - 6000000 + 12000 - 8 = 994011992$

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