Đáp án:
$\begin{array}{l}
4ab\left( {{a^2} - {b^2}} \right) - 6\left( {{a^3} + {a^2}b - a{b^2} - {b^3}} \right)\\
+ 9\left( {{a^2} - {b^2}} \right)\\
= 4ab\left( {{a^2} - {b^2}} \right) - 6.\left[ {\left( {a + b} \right).{a^2} - {b^2}\left( {a + b} \right)} \right]\\
+ 9\left( {{a^2} - {b^2}} \right)\\
= 4ab\left( {{a^2} - {b^2}} \right) - 6\left( {a + b} \right)\left( {{a^2} - {b^2}} \right) + 9\left( {{a^2} - {b^2}} \right)\\
= \left( {{a^2} - {b^2}} \right)\left( {4ab - 6a - 6b + 9} \right)\\
= \left( {a + b} \right)\left( {a - b} \right).\left( {2b - 3} \right)\left( {2a - 3} \right)
\end{array}$
