Đáp án:
$\begin{array}{l}
1)x\sqrt y - y\sqrt x \\
= \sqrt {xy} \left( {\sqrt x - \sqrt y } \right)\\
2)x + y - 2\sqrt {xy} - 81\\
= {\left( {\sqrt x - \sqrt y } \right)^2} - {9^2}\\
= \left( {\sqrt x - \sqrt y - 9} \right)\left( {\sqrt x - \sqrt y + 9} \right)\\
3)x - \sqrt x - 12\\
= \left( {\sqrt x - 4} \right)\left( {\sqrt x + 3} \right)\\
4)y + 6\sqrt y + 8\\
= y + 2\sqrt y + 4\sqrt y + 8\\
= \left( {\sqrt y + 2} \right)\left( {\sqrt y + 4} \right)\\
5)x - 9{y^2}\\
= \left( {\sqrt x - 3y} \right)\left( {\sqrt x + 3y} \right)\\
6)5 + \sqrt 5 \\
= \sqrt 5 \left( {\sqrt 5 + 1} \right)\\
7)3 + 2\sqrt 2 = {\left( {\sqrt 2 + 1} \right)^2}\\
8)5 - 2\sqrt 6 = {\left( {\sqrt 3 - \sqrt 2 } \right)^2}\\
9)\sqrt {xy} + 1 + \sqrt x + \sqrt y \\
= \sqrt x \left( {\sqrt y + 1} \right) + \left( {\sqrt y + 1} \right)\\
= \left( {\sqrt y + 1} \right)\left( {\sqrt x + 1} \right)\\
10)\sqrt 8 - \sqrt 5 - 2 + \sqrt {10} \\
= 2\sqrt 2 - \sqrt 5 - 2 + \sqrt 5 .\sqrt 2 \\
= \sqrt 2 \left( {2 + \sqrt 5 } \right) - \left( {2 + \sqrt 5 } \right)\\
= \left( {2 + \sqrt 5 } \right)\left( {\sqrt 2 - 1} \right)\\
11)\\
4 - 2\sqrt 3 = {\left( {\sqrt 3 - 1} \right)^2}\\
12)6 + 2\sqrt 5 = {\left( {\sqrt 5 + 1} \right)^2}\\
13)8 - 2\sqrt {15} = {\left( {\sqrt 5 - \sqrt 3 } \right)^2}
\end{array}$
