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

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Solution

$27 x^{3} + y^{3} + z^{3} - 9 x y z = {(3 x)}^{3} + y^{3} + z^{3} - 3 (3 x) \times y \times z$

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

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

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