If `x+y+z=0`show that `x^3+y^3+z^3=3x y z`.

If quad x+y+z=0 show that x^(3)+y^(3)+z^(3)=3xyz

If x+y+z=0 then x^3+y^3+z^3+3xyz equal to

Show that : |x y z x^2y^2z^2x^3y^3z^3|=x y z(x-y)(y-z)(z-x)dot

(i) Factorize the experssions 8a^(6)+5a^3+1 (ii) show that (x-y)^3+(z-x)^3+(z-x)^3=3(x-y)(y-z)(z-x)

If x+y+z=xyz , show that : (3x-x^3)/(1-3x^2) + (3y-y^3)/(1-3y^2) + (3z-z^3)/(1-3z^2) = (3x-x^3)/(1-3x^2) . (3y-y^3)/(1-3y^2) . (3z-z^3)/(1-3z^2)

If x + y + z = 0 , then ( x + y - z)^(3) + ( y + z - x)^(3) + (z + x - y) ^(3) = k (xyz) , where k is equal to :