Đáp án:
$\begin{array}{l}
{a^2}\left( {b - c} \right) + {c^2}\left( {a - b} \right) + {b^2}\left( {c - a} \right)\\
= {a^2}b - {a^2}c + a{c^2} - b{c^2} + {b^2}\left( {c - a} \right)\\
= {a^2}b - b{c^2} - {a^2}c + a{c^2} + {b^2}\left( {c - a} \right)\\
= b\left( {{a^2} - {c^2}} \right) - ac\left( {a - c} \right) - {b^2}\left( {a - c} \right)\\
= b\left( {a + c} \right)\left( {a - c} \right) - ac\left( {a - c} \right) - {b^2}\left( {a - c} \right)\\
= \left( {a - c} \right)\left( {ab + bc - ac - {b^2}} \right)\\
= \left( {a - c} \right).\left( {ab - {b^2} + bc - ac} \right)\\
= \left( {a - c} \right).\left( {a - b} \right)\left( {b - c} \right)\\
= \left( {b - a} \right).\left( {c - a} \right).\left( {c - b} \right)
\end{array}$
