Factorize:
</p

We know that,

a³ + b³ + c³ – 3abc = (a + b + c) (a² + b² + c² – ab – bc – ca)]

Using this formula, we get

Putting (a – b) = x, (b – c) = y and (c – a) = z, we get

(a - b)³ + (b - c)³ + (c - a)³= x³ + y³ + z³

Where (x + y + z) = (a – b) + (b – c) + (c – a) = 0

= 3xyz [Since, (x + y + z) = 0 so (x³ + y³ + z³) = 3xyz]

= 3 (a – b) (b – c) (c – a)