Factorise :
$x^{3} - 8 y^{3} - 64 z^{3} - 24 x y z$

(x - 2 y - 4 z) (x^{2} + 4 y^{2} + 16 z^{2} + x y - 8 y z + 4 x z)

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(x - 2 y - 4 z) (x^{2} + 4 y^{2} + 16 z^{2} + 2 x y - 8 y z + 4 x z)

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(4 z) (x^{2} + 4 y^{2} + 16 z^{2} + 2 x y - 8 y z + 4 x z)

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(2 y - 4 z) (x^{2} + 4 y^{2} + 16 z^{2} + 2 x y - 8 y z + 4 x z)

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Solution

The correct option is B $(x - 2 y - 4 z) (x^{2} + 4 y^{2} + 16 z^{2} + 2 x y - 8 y z + 4 x z)$
$x^{3} - 8 y^{3} - 64 z^{3} - 24 x y z$
$a^{3} + b^{3} + c^{3} - 3 a b c = (a + b + c) (a^{2} + b^{2} + c^{2} - a b - b c - c a)$
Comparing with the expression of standard formulae,
Here,
$a = x$
$b = - 2 y$
$c = - 4 z$
Therefore,
$=> x^{3} + (- 2 y)^{3} + (- 4 z)^{3} - 3 (x) (- 2 y) (- 4 z) = (x - 2 y - 4 z) (x^{2} + 4 y^{2} + 16 z^{2} + 2 x y - 8 y z + 4 x z)$

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