Expression (x^3)y + (y^3)z + (z^3)x

Show that for all real numbers   $x, \; y, \; z$   such that

$x \; + \; y \; + \; z \; = \; 0$

and

$x \, y \; + \; y \, z \; + \; z \, x \; = \; -3$

the expression   $x^3 \, y \; + \; y^3 \, z \; + \; z^3 \, x$   is a constant.