Factorise: 27 x^3-y^3-z^3-9 x y z - Vidyadip

Question

Factorise:
$27 x^3-y^3-z^3-9 x y z$

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Answer

$27 x^3-y^3-z^3-9 x y z$
$=(3 x)^3-y^3-z^3-3 \times(3 x) \times(-y) \times(-z)$
We know,
$a^3+b^3+c^3-3 a b c$
$=(a+b+c)\left(a^2+b^2+c^2-a b-b c-c a\right)$
$a=3 x, b=-y, c=-z$
$(3 x)^3-y^3-z^3-3 \times(3 x) \times(-y) \times(-z)$
$=(3 x-y-z)\left(9 x^2+y^2+z^2+3 x y-y z+3 x z\right)$

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