`#tnvt`
`a)x-\sqrt{xy}(x,y>=0)`
`=\sqrt{x}(\sqrt{x}-\sqrt{y})`
`b)x-\sqrt{x}(x>=0)`
`=\sqrt{x}(\sqrt{x}-1)`
`c)x\sqrt{y}-y\sqrt{x}(x,y>=0)`
`=\sqrt{xy}(\sqrt{x}-\sqrt{y})`
`d)x\sqrt{x}+1(x>=0)`
`=\sqrt{x}^3+1^3`
`=(\sqrt{x}+1)(x-\sqrt{x}+1)`
`e)x\sqrt{x}-y\sqrt{y}(x,y>=0)`
`=\sqrt{x^3}-\sqrt{y^3}`
`=(\sqrt{x}-\sqrt{y])(x+\sqrt{xy}+y)`
`f)x^3-\sqrt{x}`
`=\sqrt{x}(x^2\sqrt{x}-1)`
`g)xy+y\sqrt{x}+\sqrt{x}+1(x.=0)`
`=y\sqrt{x}(\sqrt{x}+1)+(\sqrt{x}+1)`
`=(\sqrt{x}+1)(y\sqrt{x}+1)`
`h)\sqrt{x^3}-\sqrt{y^3}+\sqrt{x^2y}-\sqrt{xy^2}(x,y>=0)`
`=(\sqrt{x}-\sqrt{y})(x+\sqrt{xy}+y)-\sqrt{xy}(\sqrt{x}-\sqrt{y})`
`=(\sqrt{x}-\sqrt{y})(x+\sqrt{xy}+y-\sqrt{xy})`
`=(\sqrt{x}-\sqrt{y})(x+y)`
