Factorize (a – 3b)^3 + (3b – c)^3 + (c – a)^3

Factorize the following expression : \( (a – 3b)^3 + (3b – c)^3 + (c – a)^3 \)

\[ (a – 3b)^3 + (3b – c)^3 + (c – a)^3 \] \[ \text{Let } x = (a – 3b),\quad y = (3b – c),\quad z = (c – a) \] \[ x + y + z = 0 \] \[ \therefore x^3 + y^3 + z^3 = 3xyz \] \[ = 3(a – 3b)(3b – c)(c – a) \]

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