$a^{3}$ - $b^{3}$ is always divisible by:

a - b

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a × b

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a + b

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2a + b

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Solution

The correct option is A
a - b

Take $a = 2$ and $b = 1$ and check.
Alternatively, we know the algebraic identity,

$a^{3} - b^{3} = (a - b) (a^{2} + 2 a b + b^{2}$ )

Hence , we can see that $(a - b)$ is a factor of $a^{3}$ - $b^{3}$
Thus, $a^{3}$ - $b^{3}$ is divisible by $(a - b)$

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