a) \(x-2\sqrt{x}\)
\(=\sqrt{x}\left(\sqrt{x}-2\right)\)
b) \(3x-2\sqrt{x}\)
\(=\sqrt{x}\left(3\sqrt{x}-2\right)\)
c) \(4x+2\sqrt{x}\)
\(=2\sqrt{x}\left(2\sqrt{x}+1\right)\)
d) \(x-2\sqrt{x}+1\)
\(=\left(\sqrt{x}-1\right)^2\)
e) \(x\sqrt{x}-1\)
\(=\left(\sqrt{x}\right)^3-1\)
\(=\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)\)
g) \(x\sqrt{x}+27\)
\(=\left(\sqrt{x}\right)^3+3^3\)
\(=\left(\sqrt{x}+3\right)\left(x+3\sqrt{x}+9\right)\)
h) \(x-y\)
\(=\left(\sqrt{x}-\sqrt{y}\right)\left(\sqrt{x}+\sqrt{y}\right)\)
i) \(x\sqrt{x}-y\sqrt{y}\)
\(=\left(\sqrt{x}\right)^3-\left(\sqrt{y}\right)^3\)
\(=\left(\sqrt{x}-\sqrt{y}\right)\left(x+\sqrt{xy}+y\right)\)
k) \(4x-4\sqrt{x}+1\)
\(=\left(2\sqrt{x}-1\right)^2\)
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