Question

simplify the equation
​

Answer 1

Let

a= (x^3-y^3)^3

b= (y^3-z^3)^3

c= (z^3-x^3)^3

if a+b+c=0

then a^3+b^3+c^3=3abc

Using this formula in the given equation, we get

= 3(x^3-y^3)(y^3-z^3)(z^3-x^3) / 3(x-y)(y-z)(z-x)

= (x-y)(x^2+y^2+xy)(y-z)(y^2+z^2+yz)(z-x)(z^2+x^2+zx) / (x-y)(y-z)(z-x)

= (x^2+y^2+xy)(y^2+z^2+yz)(z^2+x^2+zx)

Hope you understood :D