$\frac{z\left(x+y\right)\left(xy\left(x+z\right)\left(y+z\right)\right)^{2}}{2}$

$x^{2}\left(yz\right)^{4}+y^{2}\left(xz\right)^{4}+2z^{2}\left(xy\right)^{4}+\frac{5x^{4}\left(yz\right)^{3}}{2}+\frac{5y^{4}\left(xz\right)^{3}}{2}+2z^{4}\left(xy\right)^{3}+\frac{x^{2}y^{3}z^{5}}{2}+\frac{x^{2}z^{3}y^{5}}{2}+\frac{y^{2}x^{3}z^{5}}{2}+\frac{y^{2}z^{3}x^{5}}{2}+z^{2}x^{3}y^{5}+z^{2}y^{3}x^{5}+\frac{zx^{4}y^{5}}{2}+\frac{zy^{4}x^{5}}{2}$