2. \(x\sqrt{x}+y\sqrt{y}=\left(\sqrt{x}\right)^3+\left(\sqrt{y}\right)^3=\left(\sqrt{x}+\sqrt{y}\right)\left(x-\sqrt{xy}+y\right)\)
4. \(x-1=\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)\)
5. \(x+2\sqrt{x}+1=\left(\sqrt{x}+1\right)^2\)
7. \(x\sqrt{x}-y\sqrt{y}=\left(\sqrt{x}\right)^3-\left(\sqrt{y}\right)^3=\left(\sqrt{x}-\sqrt{y}\right)\left(x+\sqrt{xy}+y\right)\)
8. \(x\sqrt{y}-y\sqrt{x}=\sqrt{xy}\left(\sqrt{x}-\sqrt{y}\right)\)
10. \(x\sqrt{x}+\sqrt{x}-x-1=\sqrt{x}\left(x+1\right)-\left(x+1\right)=\left(x+1\right)\left(\sqrt{x}-1\right)\)
11. \(x\sqrt{x}+x+\sqrt{x}+1=x\left(\sqrt{x}+1\right)+\left(\sqrt{x}+1\right)=\left(\sqrt{x}+1\right)\left(x+1\right)\)
12. \(x\sqrt{x}-\sqrt{x}+2x-2=\sqrt{x}\left(x-1\right)+2\left(x-1\right)=\left(x-1\right)\left(\sqrt{x}+2\right)\)
13. \(\sqrt{xy}-3\sqrt{x}-5\sqrt{y}+15=\sqrt{x}\left(\sqrt{y}-3\right)-5\left(\sqrt{y}-3\right)=\left(\sqrt{y}-3\right)\left(\sqrt{x}-5\right)\)
10) \(x\sqrt{x}+\sqrt{x}-x-1=\sqrt{x}\left(x+1\right)-\left(x+1\right)=\left(x+1\right)\cdot\left(\sqrt{x}-1\right)\)
11) \(x\sqrt{x}+x+\sqrt{x}+1=x\left(\sqrt{x}+1\right)+\left(\sqrt{x}+1\right)=\left(\sqrt{x}+1\right)\left(x+1\right)\)
