Đáp án:
$\begin{array}{l}
7)\\
x{\left( {x - y} \right)^3} - y{\left( {y - x} \right)^2} - {y^2}\left( {x - y} \right)\\
= \left( {x - y} \right)\left( {x.{{\left( {x - y} \right)}^2} - y\left( {x - y} \right) - {y^2}} \right)\\
= \left( {x - y} \right).\left( {x\left( {{x^2} - 2xy + {y^2}} \right) - xy + {y^2} - {y^2}} \right)\\
= \left( {x - y} \right).\left[ {{x^3} - 2{x^2}y + x{y^2} - xy} \right]\\
9){x^2}y - x{y^2} - 3x + 3y\\
= xy\left( {x - y} \right) - 3\left( {x - y} \right)\\
= \left( {x - y} \right)\left( {xy - 3} \right)\\
11){\left( {4{x^2} - 3x - 18} \right)^2} - {\left( {4{x^2} + 3x} \right)^2}\\
= \left( {4{x^2} - 3x - 18 - 4{x^2} - 3x} \right).\left( {4{x^2} - 3x - 18 + 4{x^2} + 3x} \right)\\
= \left( { - 6x - 18} \right)\left( {8{x^2} - 18} \right)\\
= - 6\left( {x + 3} \right).2.\left( {4{x^2} - 9} \right)\\
= - 12\left( {x + 3} \right).\left( {2x - 3} \right)\left( {2x + 3} \right)\\
13) - 4{x^2} + 12xy - 9{y^2} + 25\\
= 25 - \left( {4{x^2} - 12xy + 9{y^2}} \right)\\
= {5^2} - {\left( {2x - 3y} \right)^2}\\
= \left( {5 - 2x + 3y} \right)\left( {5 + 2x - 3y} \right)\\
15){x^2} - 36{y^2} + 8x + 16\\
= {x^2} + 8x + 16 - 36{y^2}\\
= {\left( {x + 4} \right)^2} - {\left( {6y} \right)^2}\\
= \left( {x + 4 + 6y} \right)\left( {x + 4 - 6y} \right)
\end{array}$
