Solve (x-y)^{3}+(y-z)^{3}+(z-x)^3y(x-y)^3-(z-y)^3-(x-z)^3

$$( x - y ) ^ { 3 } + ( y - z ) ^ { 3 } + ( z - x ) ^ { 3 } y ( x - y ) ^ { 3 } - ( z - y ) ^ { 3 } - ( x - z ) ^ { 3 }$$

Evaluate

$$-y\left(\left(x-y\right)\left(x-z\right)\right)^{3}-\left(x-y\right)\left(\left(x-z\right)\left(y-z\right)+\left(x-z\right)^{2}+\left(y-z\right)^{2}\right)+\left(x-z\right)\left(-\left(x-y\right)\left(y-z\right)+\left(x-y\right)^{2}+\left(y-z\right)^{2}\right)$$

Expand

$$x^{3}y^{4}+9x^{3}\left(yz\right)^{2}+3xy^{2}+3xz^{2}y^{4}-3xz^{2}+3x\left(yz\right)^{3}-3y^{3}x^{4}-9y^{3}\left(xz\right)^{2}+y^{3}+3y^{2}x^{5}-yx^{6}-3yx^{2}-3yz^{2}x^{4}+6yz^{2}+3yzx^{5}+y\left(xz\right)^{3}-z^{3}y^{4}-3z^{3}\left(xy\right)^{2}-z^{3}-3zx^{2}y^{4}+3zx^{2}-9zy^{2}x^{4}-6zy^{2}+9z\left(xy\right)^{3}$$