Short answer type questions:

Let us write the simplest value of

Let p = (b² – c²), q = (c² – a²) and r = (a² – b²)

Since p + q+ r = 0 and we have an identity that if,

x + y + z = 0, the x³ + y³ + z ³ = 3xyz

⇒ p³ + q³ + r³ = 3pqr

Similarly in denominator of given fraction, we see that sum of all the individual terms is equal to 0, so same identity can be applied in denominator as well.

The fractions reduces to:

Also as, x² – y² = (x - y)(x + y)