1: \(x+\sqrt{x}=\sqrt{x}\left(\sqrt{x}+1\right)\)
2: \(3x-3\sqrt{x}=3\sqrt{x}\left(\sqrt{x}-1\right)\)
3: \(x-y=\left(\sqrt{x}-\sqrt{y}\right)\left(\sqrt{x}+\sqrt{y}\right)\)
4: \(36\sqrt{x}-x\cdot\sqrt{x}=\sqrt{x}\left(36-x\right)=\sqrt{x}\left(6-\sqrt{x}\right)\left(6+\sqrt{x}\right)\)
5: \(x-4=\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)\)
6: \(x\sqrt{x}-y\cdot\sqrt{x}=\sqrt{x}\left(x-y\right)=\sqrt{x}\left(\sqrt{x}-\sqrt{y}\right)\left(\sqrt{x}+\sqrt{y}\right)\)
7: \(x-3\sqrt{x}+2=x-\sqrt{x}-2\sqrt{x}+2\)
\(=\sqrt{x}\left(\sqrt{x}-1\right)-2\left(\sqrt{x}-1\right)=\left(\sqrt{x}-1\right)\left(\sqrt{x}-2\right)\)
8: \(x-\sqrt{x}-2\)
\(=x-2\sqrt{x}+\sqrt{x}-2\)
\(=\sqrt{x}\left(\sqrt{x}-2\right)+\left(\sqrt{x}-2\right)=\left(\sqrt{x}-2\right)\left(\sqrt{x}+1\right)\)
9: \(3x-\sqrt{x}-2=3x-3\sqrt{x}+2\sqrt{x}-2\)
\(=3\sqrt{x}\left(\sqrt{x}-1\right)+2\left(\sqrt{x}-1\right)=\left(\sqrt{x}-1\right)\left(3\sqrt{x}+2\right)\)
10: \(x+y+2\sqrt{xy}=\left(\sqrt{x}+\sqrt{y}\right)^2\)
