Is this expression a perfect square?

Question

Show that the expression $$(x^2-yz)^3+(y^2-zx)^3+(z^2-xy)^3-3(x^2-yz)(y^2-zx)(z^2-xy)$$ is a perfect square and Find its square root.

Answer 1

$$(x^2 - yz)^3 + (y^2 - zx)^3 + (z^2 - xy)^3 - 3 (x^2 - yz) (y^2 - zx) (z^2 - xy) =(x^3 + y^3 - 3 x y z + z^3)^2$$

Answer 2

The given expression can be factored as $$[(x+y+z)(x^2+y^2+z^2-xy-yz-zx)]^2.$$