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\(-\sqrt{x}+x-2\)
\(=x-\sqrt{x}-2=x+\sqrt{x}-2\sqrt{x}-2\)
\(=\sqrt{x}\left(\sqrt{x}+1\right)-2\left(\sqrt{x}+1\right)\)
\(=\left(\sqrt{x}+1\right)\left(\sqrt{x}-2\right)\)
cái trên thì chịu
cái dưới <=> \(\sqrt{xy}\left(\sqrt{x}+\sqrt{y}\right)+\left(\sqrt{x}+\sqrt{y}\right)\left(\sqrt{x}-\sqrt{y}\right)=\left(\sqrt{x}+\sqrt{y}\right)\left(\sqrt{xy}+\sqrt{x}-\sqrt{y}\right)\)
a) \(x-2\sqrt{x-1}-a^2=\left(x-1\right)-2\sqrt{x-1}+1-a^2=\left(\sqrt{x-1}-1\right)^2-a^2=\left(\sqrt{x-1}-a-1\right)\left(\sqrt{x-1}+a-1\right)\)
b) \(x\sqrt{x}+y\sqrt{y}+x-y=\left(\sqrt{x}+\sqrt{y}\right)\left(x-\sqrt{xy}+y\right)+\left(\sqrt{x}-\sqrt{y}\right)\left(\sqrt{x}+\sqrt{y}\right)=\left(\sqrt{x}+\sqrt{y}\right)\left(x-\sqrt{xy}+y+\sqrt{x}-\sqrt{y}\right)\)
\(\sqrt{ab}-\sqrt{a}-\sqrt{b}+1\)
\(=\sqrt{a}\left(\sqrt{b}-1\right)-\left(\sqrt{b}-1\right)\)
\(=\left(\sqrt{a}-1\right)\left(\sqrt{b}-1\right)\)
\(\sqrt{ab}-\sqrt{a}-\sqrt{b}+1=\sqrt{a}\left(\sqrt{b}-1\right)-\left(\sqrt{b}-1\right)=\left(\sqrt{a}-1\right)\left(\sqrt{b}-1\right)\)
\(=\sqrt{a}\left(\sqrt{a}+1\right)+2\sqrt{b}\left(\sqrt{a}+1\right)=\left(\sqrt{a}+1\right)\left(\sqrt{a}+2\sqrt{b}\right)\)
\(xy-y\sqrt{x}+\sqrt{x}-1\)
\(=y\left(x-\sqrt{x}\right)+\left(\sqrt{x}-1\right)\)
\(=y\sqrt{x}\left(\sqrt{x}-1\right)+\left(\sqrt{x}-1\right)\)
\(\left(\sqrt{x}-1\right)\left(y\sqrt{x}+1\right)\)