Giải thích các bước giải:
$\begin{array}{l}
a){a^3} + {b^3} + {c^3} - 3abc\\
= \left( {{a^3} + {b^3}} \right) + {c^3} - 3abc\\
= {\left( {a + b} \right)^3} - 3ab\left( {a + b} \right) + {c^3} - 3abc\\
= {\left( {a + b} \right)^3} + {c^3} - 3ab\left( {a + b + c} \right)\\
= \left( {a + b + c} \right)\left( {{{\left( {a + b} \right)}^2} - \left( {a + b} \right)c + {c^2}} \right) - 3ab\left( {a + b + c} \right)\\
= \left( {a + b + c} \right)\left( {{{\left( {a + b} \right)}^2} - \left( {a + b} \right)c + {c^2} - 3ab} \right)\\
= \left( {a + b + c} \right)\left( {{a^2} + {b^2} + {c^2} - ab - ac - bc} \right)\\
b){\left( {x - y} \right)^3} + {\left( {y - z} \right)^3} + {\left( {z - x} \right)^3}\\
= \left( {x - y + y - z + z - x} \right)\left( {{{\left( {x - y} \right)}^2} + {{\left( {y - z} \right)}^2} + {{\left( {z - x} \right)}^2} - \left( {x - y} \right)\left( {y - z} \right) - \left( {y - z} \right)\left( {z - x} \right) - \left( {z - x} \right)\left( {x - y} \right)} \right) + 3\left( {x - y} \right)\left( {y - z} \right)\left( {z - x} \right)\\
= 0.\left( {{{\left( {x - y} \right)}^2} + {{\left( {y - z} \right)}^2} + {{\left( {z - x} \right)}^2} - \left( {x - y} \right)\left( {y - z} \right) - \left( {y - z} \right)\left( {z - x} \right) - \left( {z - x} \right)\left( {x - y} \right)} \right) + 3\left( {x - y} \right)\left( {y - z} \right)\left( {z - x} \right)\\
= 3\left( {x - y} \right)\left( {y - z} \right)\left( {z - x} \right)
\end{array}$
