Let's simplify
`(X^3 + y^3 (x^3 - y^3) + (y^3 + z^3) (y^3 - z^3) + (z^3 + x^3) (x^3 - x^3)`

x^(3)-8(y-z)^(3)

If x, y, z are positive quantities, prove that frac(x^3 + y^3)(x + y) + frac(y^3 + z^3)(y + z) + frac(z^3 + x^3)(z + x) ge xy + yz + zx

Let's write the value of x^3 - y^3 -z^3 - 3xyz if x = y + z

(x-y)^(3)+(y-z)^(3)+(z-x)^(3)

If (x^3 -y^3) prop (x^3 +y^3) then prove that (x - y) prop ( x + y)

Verify that x ^(3) + y ^(3) + z ^(3) - 3xyz =1/2 (x + y + z) [(x-y)^(2) + (y-z) ^(2) + (z-x) ^(2) ]

If x+y+z=xyz then prove 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)

(a) If x + y + z=0, show that x ^(3) + y ^(3) + z ^(3)= 3 xyz. (b) Show that (a-b)^(3) + (b-c) ^(3) + (c-a)^(3) =3 (a-b) (b-c) (c-a)

Answer any one question : If x : a = y : b = z : c, then show that (x^3)/(a^3) + (y^3)/(b^3) + (z^3)/(c^3) = (3xyz)/(abc) .

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