Factorise: $27 x^{3} + y^{3} + z^{3} - 9 x yz$

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Factorise:

27 x^{3} + y^{3} + z^{3} - 9 x yz

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27 x^{3} + y^{3} + z^{3} - 9 x yz

= (3 x)^{3} + (y)^{3} + z^{3} - 3 (3 x) (y) (z)

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

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

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