One of the factors of $a^{3} + 8 b^{3} - 64 c^{3} + 24 a b c$ is

a + 2 b - 4 c

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a - 2 b + 4 c

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a + 2 b + 4 c

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a - 2 b - 4 c

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Solution

The correct option is B $a + 2 b - 4 c$
$a^{3} + 8 b^{3} - 64 c^{3} + 24 a b c$
$= (a)^{3} + (2 b)^{3} + (- 4 c)^{3} - 3 (a) (2 b) (- 4 c)$
$= (a + 2 b - 4 c) (a^{2} + 4 b^{2} + 16 c^{2} - 2 a b + 8 b c - 4 a c)$

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