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

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Solution

Consider the given equation we get

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

${(3 x)}^{3} + y^{3} + z^{3} - 9 x y z = 0$

$∵ A^{3} + B^{3} + C^{3} - 3 A B C = (A + B + C) (A^{2} + B^{2} + C^{2} - A B - B C - C A)$

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

Hence this is the answer .

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