Question

(x²-y²)³+(y²-z²)³+(z²-x²)³/(x-y)³+(y-z)³+(z-x)³ evaluate

Answer 1

We use the fact that if x+y+z = 0, then x³+y³+ z³ = 3 x y z.

(x²-y²) + (y²-z²) + (z²-x²)  = 0
also: (x-y) + (y-z)+ (z-x) = 0
we assume that:  x ≠y ≠ z.


hence,

(x²-y²)³ + (y²-z²)³ + (z²-x²)³  ÷  (x-y)³ + (y-z)³ + (z-x)³
=  3 (x²-y²) (y²-z²) (z²-x²) ÷ [3 (x-y) (y-z) (z-x)]
=  (x+y) (y+z) (z+x)