Evaluate :

(a - b)³ + (b - c)³ + (c - a)³ by writing answer in factors form.

We use the identity:

x³ + y³ + z³ = 3xyz, if x + y + z = 0

Let (a - b) = x, (b - c) = y and (c - a) = z.

Then, x + y + z = a - b + b - c + c - a = 0

Since the sum is zero, we apply the identity:

⇒ (a - b)³ + (b - c)³ + (c - a)³ = 3(a - b)(b - c)(c - a)

Hence, (a - b)³ + (b - c)³ + (c - a)³ = 3(a - b)(b - c)(c - a).