Factorize 27x^3 – y^3 – z^3 – 9xyz

Factorize the following expression : \( 27x^3 – y^3 – z^3 – 9xyz \)

\[ 27x^3 – y^3 – z^3 – 9xyz \] \[ = (3x)^3 + (-y)^3 + (-z)^3 – 3(3x)(-y)(-z) \] \[ = \left[(3x) + (-y) + (-z)\right] \left[ (3x)^2 + (-y)^2 + (-z)^2 – (3x)(-y) – (-y)(-z) – (-z)(3x) \right] \] \[ = (3x – y – z) (9x^2 + y^2 + z^2 + 3xy – yz + 3xz) \]

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