Đáp án
$\begin{array}{l}
(x + y).({x^2} - {y^2}) + (y + z).({y^2} - {z^2}) + (z + x)({z^2} - {x^2})\\
= {x^3} - x{y^2} + {x^2}y - {y^3} + {y^3} - y{z^2} + {y^2}z - {z^3} + {z^3} - {x^2}z + x{z^2} - {x^3}\\
= - x{y^2} + {x^2}y - y{z^2} + {y^2}z - {x^2}z + x{z^2}\\
= (x{z^2} - x{y^2}) + ( - y{z^2} + {y^2}z) + ({x^2}y - {x^2}z)\\
= x({z^2} - {y^2}) + yz(y - z) + {x^2}(y - z)\\
= (y - z){\rm{[ - x(y + z) + yz + }}{{\rm{x}}^2}{\rm{]}}\\
= (y - z){\rm{[}}{{\rm{x}}^2} + yz - xy - xz]
\end{array}$
