Đáp án:
$\begin{array}{l}
{x^2}{y^2}\left( {x - y} \right) + {y^2}{z^2}\left( {y - z} \right) - {z^2}{x^2}\left( {z - x} \right)\\
= {x^3}{y^2} - {x^2}{y^3} + {y^3}{z^2} - {y^2}{z^3} - {z^2}{x^2}\left( {z - x} \right)\\
= \left( {{x^3}{y^2} - {y^2}{z^3}} \right) + \left( {{y^3}{z^2} - {x^2}{y^3}} \right) - {z^2}{x^2}\left( {z - x} \right)\\
= {y^2}\left( {{x^3} - {z^3}} \right) + {y^3}\left( {{z^2} - {x^2}} \right) - {z^2}{x^2}\left( {z - x} \right)\\
= {y^2}\left( {x - z} \right)\left( {{x^2} + xz + {z^2}} \right) + {y^3}\left( {z - x} \right)\left( {z + x} \right)\\
- {z^2}{x^2}\left( {z - x} \right)\\
= \left( {x - z} \right).\left( {{x^2}{y^2} + xz{y^2} + {y^2}{z^2} - {y^3}z - x{y^3} + {z^2}{x^2}} \right)\\
= \left( {x - z} \right).\left( {{x^2}{y^2} + {y^2}{z^2} + {x^2}{z^2} + xz{y^2} - {y^3}z - x{y^3}} \right)
\end{array}$
