Factorise: $8 x^{3} + y^{3} + 27 z^{3} - 18 x y z$

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

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

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

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

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Solution

The correct option is A $(2 x + y + 3 z) (4 x^{2} + y^{2} + 9 z^{2} - 2 x y - 3 y z - 6 z x)$
$8 x^{3} + y^{3} + 27 z^{3} - 18 x y z$
using the formula, $a^{3} + b^{3} + c^{3} - 3 a b c = (a + b + c) (a^{2} + b^{2} + c^{2} - a b - b c - a c)$
$= (2 x)^{3} + y^{3} + (3 z)^{3} - 3 \times 2 x \times y \times 3 z$
$= (2 x + y + 3 z) [(2 x)^{2} + y^{2} + (3 z)^{2} - 2 x \times y - y \times 3 z - 3 z \times 2 x]$
$= (2 x + y + 3 z) (4 x^{2} + y^{2} + 9 z^{2} - 2 x y - 3 y z - 6 z x)$

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