If p,q,r are all real numbers then (p - q)³ + (q - r)³ + (r - p)³ is equal to :

A. (p - q) (q - r) (r - p)

B. 3(p - q) (q - r) (r - p)

C. 1

D. 0

Answer: Option B

Solution(By Examveda Team)

Let a = p - q, b = q - r, c = r - p
∴ a + b + c = p - q + q - r + r - p
⇒ a + b + c = 0
∴ a³ + b³ + c³ = 3abc
⇒ a³ + b³ + c³ = 3(p - q) (q - r) (r - p)