If x, y, and z are said to be the real numbers, then what is the value of (x - y)³ + (y - z)³ + (z - x)³?

Question: If x, y, and z are said to be the real numbers, then what is the value of (x - y)³ + (y - z)³ + (z - x)³?

Solution:
Suppose a = (x - y), b = (y - z), and c = (z - x)
On adding a, b, and c we will get
a + b + c = x - y + y - z + z - x
∴ a + b + c =0

So, a³ + b³ + c³ = 3abc [because if a + b + c = 0, then a³ + b³ + c³ = 3abc]

We can say that (x - y)³ + (y - z)³ + (z - x)³ = 3(x - y)(y - z)(z - x)