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

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Solution

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

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

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

using identity

$a^{3} + b^{3} + c^{3} - 3 a b c = (a + b + c) (a^{2} + b^{2} + c^{2} - a b - b c - c a)$

Putting $a = 3 x, b = y, c = z$

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

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