Question

Answer 1

\(a,=5x+5\sqrt{x}+7\sqrt{x}+7\\ =5\sqrt{x}\left(\sqrt{x}+1\right)+7\left(\sqrt{x}+1\right)=\left(5\sqrt{x}+7\right)\left(\sqrt{x}+1\right)\\ b,=\sqrt{a}\left(1+\sqrt{b}\right)+\left(1+\sqrt{b}\right)=\left(\sqrt{a}+1\right)\left(\sqrt{b}+1\right)\\ c,=\left(12\sqrt{10}-9\sqrt{2}\right)+\left(4\sqrt{5}-3\right)\\ =3\sqrt{2}\left(4\sqrt{5}-3\right)+\left(4\sqrt{5}-3\right)\\ =\left(3\sqrt{2}+1\right)\left(4\sqrt{5}-3\right)\\ d,=\left(\sqrt{a}\right)^2-2\sqrt{a}\sqrt{5}+\left(\sqrt{5}\right)^2=\left(\sqrt{a}-\sqrt{5}\right)^2\)