Question

Answer 1

\(A=\left(\sqrt{x}-\sqrt{y}\right)\left(\sqrt{x}+\sqrt{y}\right)-3\left(\sqrt{x}+\sqrt{y}\right)=\left(\sqrt{x}+\sqrt{y}\right)\left(\sqrt{x}-\sqrt{y}-3\right)\\ B=\left(\sqrt{x}-2\right)^2\\ C=\left(\sqrt{x}-\sqrt{y}\right)\left(x+\sqrt{xy}+y\right)+\sqrt{xy}\left(\sqrt{x}-\sqrt{y}\right)\\ =\left(\sqrt{x}-\sqrt{y}\right)\left(x+2\sqrt{xy}+y\right)\\ =\left(\sqrt{x}-\sqrt{y}\right)\left(\sqrt{x}+\sqrt{y}\right)^2\\ D=5x^2-5x\sqrt{y}-2x\sqrt{y}+2y\\ =5x\left(x-\sqrt{y}\right)-2\sqrt{y}\left(x-\sqrt{y}\right)\\ =\left(5x-2\sqrt{y}\right)\left(x-\sqrt{y}\right)\)