Evaluate the following using suitable identities.
$(105)^{3}$

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Solution

$(105)^{3} = (100 + 5)^{3}$

$= (100)^{3} + (5)^{3} + 3 (100) (5) (100 + 5) . . . . . . . . . . . . . (∵ (x + y)^{3} = x^{3} + y^{3} + 3 x y (x + y))$

$= 1000000 + 125 + 1500 (105)$

$= 1000000 + 125 + 157500 = 1157625$

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