Evaluate the following using suitable identities.
$(1001)^{3}$

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Solution

$(1001)^{3} = (1000 + 1)^{3}$
Suitable identities is $(x + y)^{3} = x^{3} + 3 x^{2} y + 3 x y^{2} + y^{3}$
$∴ (1000 + 1)^{3}$
$= (1000)^{3} + 3 (1000)^{2} (1) + 3 (1000) (1)^{2} + (1)^{3}$
$= 1000000000 + 3000000 + 3000 + 1 = 1003003001$

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