Question 11
Factorise:
$27 x^{3} + y^{3} + z^{3} - 9 x y z$

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Solution

$\Rightarrow 27 x^{3} + y^{3} + z^{3} - 9 x y z = (3 x)^{3} + y^{3} + z^{3} - 3 (3 x) y z [U s i n g t h e i d e n t i t y a^{3} + b^{3} + c^{3} - 3 a b c = (a + b + c) (a^{2} + b^{2} + c^{2} - a b - b c - c a), w e g e t]$
$= (3 x + y + z) (9 x^{2} + y^{2} + z^{2} - 3 x y - y z - 3 z x)$

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