Phân tích mỗi đa thức sau thành nhân tử:

\(xy\left( {x + y} \right) - yz\left( {y + z} \right) + xz\left( {x - z} \right)\)

\( = {x^2}y + x{y^2} - {y^2}z - y{z^2} + xz\left( {x - z} \right)\)

\( = \left( {{x^2}y - y{z^2}} \right) + \left( {x{y^2} - {y^2}z} \right) + xz\left( {x - z} \right)\)

\( = y\left( {{x^2} - {z^2}} \right) + {y^2}\left( {x - z} \right) + xz\left( {x - z} \right)\)

\( = y\left( {x - z} \right)\left( {x + z} \right) + {y^2}\left( {x - z} \right) + xz\left( {x - z} \right)\)

\( = \left( {x - z} \right)\left( {xy + yz + {y^2} + xz} \right)\)

\( = \left( {x - z} \right)\left[ {\left( {xy + xz} \right) + \left( {yz + {y^2}} \right)} \right]\)

\( = \left( {x - z} \right)\left[ {x\left( {y + z} \right) + y\left( {y + z} \right)} \right]\)

\( = \left( {x - z} \right)\left( {y + z} \right)\left( {x + y} \right)\).