\(x\sqrt{x}+x-y+y\sqrt{x}-xy\sqrt{x}-xy\sqrt{y}=\left(x\sqrt{y}+y\sqrt{x}\right)+\left(x-y\right)-\left(xy\sqrt{x}+xy\sqrt{y}\right)\)
\(=\sqrt{xy}\left(\sqrt{x}+\sqrt{y}\right)+\left(\sqrt{x}+\sqrt{y}\right)\left(\sqrt{x}-\sqrt{y}\right)-xy\left(\sqrt{x}+\sqrt{y}\right)\)
\(=\left(\sqrt{x}+\sqrt{y}\right)\left(\sqrt{xy}+\sqrt{x}-\sqrt{y}-xy\right)\)