What is the value of $5^{3} - 1^{3}$ (without solving the cubes)?

124

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214

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224

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314

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Solution

The correct option is A $124$
Value of $5^{3} - 1^{3}$
Using $a^{3} - b^{3} = (a - b) (a^{2} + a b + b^{2})$
$\Rightarrow 5^{3} - 1^{3} = (5 - 1) (5^{2} + (5.1) + 1^{2})$
$= 4 (25 + 5 + 1)$
$= 4 (31)$
$= 124.$
Hence, the answer is $124.$

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