\(\begin{array}{l}
:a,5{x^2}(x - 1) + 10xy(x - 1) - 5{y^2}(1 - x)\\
= 5\left( {x - 1} \right)\left( {{x^2} + 2{\rm{x}}y + {y^2}} \right)\\
= 5\left( {x - 1} \right){\left( {x + y} \right)^2}\\
b,{x^5} - {x^4}y - x{y^4} + {y^5}\\
= \left( {{x^5} + {y^5}} \right) - xy\left( {{x^3} + {y^3}} \right)\\
= \left( {x + y} \right)\left( {{x^4} - {x^3}y + {x^2}{y^2} - x{y^3} + {y^4}} \right) - xy\left( {x + y} \right)\left( {{x^2} - xy + {y^2}} \right)\\
= \left( {x + y} \right)\left( {{x^4} - {x^3}y + {x^2}{y^2} - x{y^3} + {y^4} - {x^3}y + {x^2}{y^2} - x{y^3}} \right)\\
= \left( {x + y} \right)\left( {{x^4} - 2{{\rm{x}}^3}y + 2{{\rm{x}}^2}{y^2} - 2{\rm{x}}{y^3} + {y^4}} \right)\\
c,{x^6}y - {x^4}{y^3} - {x^3}{y^4} + x{y^6}\\
= xy\left( {{x^5} + {y^5}} \right) - {x^3}{y^3}\left( {x + y} \right)\\
= xy\left( {x + y} \right)\left( {{x^4} - {x^3}y + {x^2}{y^2} - x{y^3} + {y^4}} \right) - {x^3}{y^3}\left( {x + y} \right)\\
= xy\left( {x + y} \right)\left( {{x^4} - {x^3}y + {x^2}{y^2} - x{y^3} + {y^4} - {x^3}{y^2} - {x^2}{y^3}} \right)\\
d,{x^3}{y^3}{z^3} + {x^2}{y^2}{z^2} - xyz - 1\\
= {x^2}{y^2}{z^2}\left( {xyz + 1} \right) - \left( {xyz + 1} \right)\\
= \left( {xyz + 1} \right)\left( {{x^2}{y^2}{z^2} - 1} \right)\\
= \left( {xyz + 1} \right)\left( {xyz - 1} \right)\left( {xyz + 1} \right)\\
= {\left( {xyz + 1} \right)^2}\left( {xyz - 1} \right)\\
e,25{x^2} - {y^2} + 4y - 4\\
= 25{{\rm{x}}^2} - \left( {{y^2} - 4y + 4} \right)\\
= {\left( {5{\rm{x}}} \right)^2} - {\left( {y - 2} \right)^2}\\
= \left( {5{\rm{x}} - y + 2} \right)\left( {5{\rm{x}} + y - 2} \right)\\
f,{x^{(m + 1)}} - {x^m} - x + 1\\
= {x^m}\left( {x - 1} \right) - \left( {x - 1} \right)\\
= \left( {x - 1} \right)\left( {{x^m} - 1} \right)
\end{array}\)