a: \(=\sqrt{3}\left(\sqrt{3}-1\right)-\sqrt{15}\left(\sqrt{3}-1\right)\)
\(=\sqrt{3}\left(\sqrt{3}-1\right)\left(1-\sqrt{5}\right)\)
b: \(=\sqrt{1-a}\left(1+\sqrt{1+a}\right)\)
c: \(=a\sqrt{a}-b\sqrt{b}+a\sqrt{b}-b\sqrt{a}\)
\(=\left(\sqrt{a}-\sqrt{b}\right)\left(a+\sqrt{ab}+b\right)+\sqrt{ab}\left(\sqrt{a}-\sqrt{b}\right)\)
\(=\left(\sqrt{a}-\sqrt{b}\right)\left(\sqrt{a}+\sqrt{b}\right)^2\)
a. ... = \(\sqrt{3}\left(\sqrt{3}-1\right)-\sqrt{15}\left(\sqrt{3}-1\right)\) = \(\sqrt{3}\left(1-\sqrt{5}\right)\left(\sqrt{3}-1\right)\)
b. ... = \(\sqrt{1-a}+\sqrt{1-a^2}\left(-1< a< 1\right)\) \(=\left(\sqrt{1+a}+1\right)\sqrt{1-a}\)
c. ... = \(a\sqrt{a}-b\sqrt{b}+a\sqrt{b}-b\sqrt{a}=\left(\sqrt{a}-\sqrt{b}\right)\left(a+\sqrt{ab}+b\right)+\sqrt{ab}\left(\sqrt{a}-\sqrt{b}\right)\) = \(\left(\sqrt{a}-\sqrt{b}\right)\left(\sqrt{a}+\sqrt{b}\right)^2\)
d. ... = \(x-y+y\left(\sqrt{x}-\sqrt{y}\right)=\left(\sqrt{x}-\sqrt{y}\right)\left(\sqrt{x}+\sqrt{y}+y\right)\)
