a) \(a^3-2\sqrt{2}\)
\(=a^3-\left(\sqrt{2}\right)^3\)
\(=\left(a-\sqrt{2}\right)\left(a+a\sqrt{2}+2\right)\)
b) \(\sqrt{21}+\sqrt{3}+\sqrt{7}+1\)
\(=\sqrt{3}\left(\sqrt{7}+1\right)+\left(\sqrt{7}+1\right)\)
\(=\left(\sqrt{7}+1\right)\left(\sqrt{3}+1\right)\)
c) \(x+2\sqrt{x}-3\)
\(=x-\sqrt{x}+3\sqrt{x}-3\)
\(=\sqrt{x}\left(\sqrt{x}-1\right)+3\left(\sqrt{x}-1\right)\)
\(=\left(\sqrt{x}-1\right)\left(\sqrt{x}+3\right)\)