Đáp án:
$\begin{array}{l}
a){x^3} + {x^2}z + {y^2}z - xyz + {y^3}\\
= {x^3} + {y^3} + {x^2}z + {y^2}z - xyz\\
= \left( {x + y} \right)\left( {{x^2} - xy + {y^2}} \right) + z\left( {{x^2} - xy + {y^2}} \right)\\
= \left( {{x^2} - xy + {y^2}} \right)\left( {x + y + z} \right)\\
b)bc\left( {b + c} \right) + ca\left( {c - a} \right) - ab\left( {a + b} \right)\\
= {b^2}c + b{c^2} + a{c^2} - {a^2}c - ab\left( {a + b} \right)\\
= {b^2}c - {a^2}c + b{c^2} + a{c^2} - ab\left( {a + b} \right)\\
= c\left( {b - c} \right)\left( {a + b} \right) + {c^2}\left( {a + b} \right) - ab\left( {a + b} \right)\\
= \left( {a + b} \right)\left( {bc - {c^2} + {c^2} - ab} \right)\\
= \left( {a + b} \right).b.\left( {c - a} \right)\\
c){a^2}\left( {b - c} \right) + {b^2}\left( {c - a} \right) + {c^2}\left( {a - b} \right)\\
= {a^2}b - {a^2}c + {b^2}c - a{b^2} + {c^2}\left( {a - b} \right)\\
= {a^2}b - a{b^2} + {b^2}c - {a^2}c + {c^2}\left( {a - b} \right)\\
= ab\left( {a - b} \right) - c\left( {a + b} \right)\left( {a - b} \right) + {c^2}\left( {a - b} \right)\\
= \left( {a - b} \right)\left( {ab - ac - bc + {c^2}} \right)\\
= \left( {a - b} \right)\left( {b - c} \right)\left( {a - c} \right)\\
d){a^6} - {a^4} + 2{a^3} + 2{a^2}\\
= {a^4}\left( {{a^2} - 1} \right) + 2{a^2}\left( {a + 1} \right)\\
= {a^4}\left( {a - 1} \right)\left( {a + 1} \right) + 2{a^2}\left( {a + 1} \right)\\
= {a^2}\left( {a + 1} \right)\left( {{a^2}\left( {a - 1} \right) + 2} \right)\\
= {a^2}\left( {a + 1} \right)\left( {{a^3} - {a^2} + 2} \right)
\end{array}$
