Factorise :
$8 x^{3} + 27 y^{3} + 125 z^{3} - 90 x y z$

(x - 3 y + 5 z) (4 x^{2} + y^{2} + 25 z^{2} + 6 x y - 15 y z - 10 x z)

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(2 x + 3 y + 5 z) (4 x^{2} + 9 y^{2} + 5 z^{2} + 6 x y - y z - 10 x z)

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(2 x + 3 y + 5 z) (4 x^{2} + 9 y^{2} + 25 z^{2} + 6 x y - 15 y z - 10 x z)

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(x + y - 5 z) (4 x^{2} + 9 y^{2} + 25 z^{2} + x y - 15 y z - 10 x z)

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Solution

The correct option is C $(2 x + 3 y + 5 z) (4 x^{2} + 9 y^{2} + 25 z^{2} + 6 x y - 15 y z - 10 x z)$
$8 x^{3} + 27 y^{3} + 125 z^{3} - 90 x y z$
Using,
$a^{3} + b^{3} + c^{3} - 3 a b c = (a + b + c) (a^{2} + b^{2} + c^{2} - a b - b c - c a)$
Here,
$a = 2 x$
$b = 3 y$
$c = 5 z$ ,
Therefore,
$=> (2 x)^{3} + (3 y)^{3} + (5 z)^{3} - 3 \times 2 x \times 3 y \times 5 z = (2 x + 3 y + 5 z) (4 x^{2} + 9 y^{2} + 25 z^{2} + 6 x y - 15 y z - 10 x z)$

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