Đáp án:
$\begin{array}{l}
{\left( {{x^2} + {y^2}} \right)^3} - {\left( {{z^2} - {x^2}} \right)^3} - {\left( {{y^2} + {z^2}} \right)^3}\\
= {\left( {{x^2} + {y^2}} \right)^3} - {\left( {{y^2} + {z^2}} \right)^3} - {\left( {{z^2} - {x^2}} \right)^3}\\
= \left( {{x^2} + {y^2} - {y^2} - {z^2}} \right)\\
.\left[ {{{\left( {{x^2} + {y^2}} \right)}^2} + \left( {{x^2} + {y^2}} \right)\left( {{y^2} + {z^2}} \right) + {{\left( {{y^2} + {z^2}} \right)}^2}} \right]\\
- {\left( {{z^2} - {x^2}} \right)^3}\\
= \left( {{x^2} - {z^2}} \right).\\
\left( \begin{array}{l}
{x^4} + 2{x^2}{y^2} + {y^4} + {x^2}{y^2} + {x^2}{z^2}\\
+ {y^4} + {y^2}{z^2} + {y^4} + 2{y^2}{z^2} + {z^4}
\end{array} \right)\\
+ {\left( {{x^2} - {z^2}} \right)^3}\\
= \left( {{x^2} - {z^2}} \right).\left( \begin{array}{l}
{x^4} + 3{y^4} + {z^4} + 3{x^2}{y^2} + 3{y^2}{z^2} + {x^2}{z^2}\\
+ {\left( {{x^2} - {z^2}} \right)^2}
\end{array} \right)\\
= \left( {x - z} \right)\left( {x + z} \right)\\
.\left( {2{x^4} + 3{y^4} + 2{z^4} + 3{x^2}{y^2} + 3{y^2}{z^2} - {x^2}{z^2}} \right)
\end{array}$
