$15^{3} - 8^{3}$ is divisible by _____

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Solution

The correct option is B 7
{ $a^{3} - b^{3} = (a - b) (a^{2} + b^{2} + a b)$ }
$15^{3} - 8^{3}$
$= (15 - 8) (15^{2} + 15 \times 8 + 8^{2})$
$= 7 (225 + 120 + 64)$
$= 7 (409)$
Since,the final value is a multiple of 7.
hence
$15^{3} - 8^{3}$ is a divisible by 7

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