\(\begin{array}{l}
a)\, = {x^2}y - {x^2}z + {y^2}z - {y^2}x + {z^2}\left( {x - y} \right)\\
 = xy\left( {x - y} \right) - z\left( {{x^2} - {y^2}} \right) + {z^2}\left( {x - y} \right)\\
 = \left( {x - y} \right)\left( {xy - zx - zy + {z^2}} \right)\\
 = \left( {x - y} \right)\left( {x\left( {y - z} \right) - z\left( {y - z} \right)} \right)\\
 = \left( {z - y} \right)\left( {x - z} \right)\left( {y - z} \right)\\
b)\, = {\left( {a - b} \right)^2} - {\left( {c + d} \right)^2}\\
 = \left( {a - b + c + d} \right)\left( {a - b - c - d} \right)\\
c)\, = {x^3}\left( {x - 1} \right) - \left( {x - 1} \right)\left( {x + 1} \right)\\
 = \left( {x - 1} \right)\left( {{x^3} - x - 1} \right)\\
d)\,\left( {y + z} \right)\left( {{{\left( {x + y + z} \right)}^2} + x\left( {x + y + z} \right) + {x^2}} \right) - \left( {y + z} \right)\left( {{y^2} - yz + {z^2}} \right)\\
 = \left( {y + z} \right)\left( {3{x^2} + {y^2} + {z^2} + 3xy + 2yz + 3xz - {y^2} + yz - {z^2}} \right)\\
 = \left( {y + z} \right)3\left( {{x^2} + xy + yz + xz} \right)\\
 = 3\left( {y + z} \right)\left( {x\left( {x + y} \right) + z\left( {x + y} \right)} \right)\\
 = 3\left( {y + z} \right)\left( {x + y} \right)\left( {x + z} \right)\\
e)\,{x^6} - {y^6} = \left( {{x^2} - {y^2}} \right)\left( {{x^4} + {x^2}{y^2} + {y^4}} \right)\\
 = \left( {x - y} \right)\left( {x + y} \right)\left( {{x^4} + {x^2}{y^2} + {y^4}} \right)\\
f)\, = {x^4} + 5{x^2} - {x^2} - 5\\
 = {x^2}\left( {{x^2} + 5} \right) - \left( {{x^2} + 5} \right)\\
 = \left( {x - 1} \right)\left( {x + 1} \right)\left( {{x^2} + 5} \right)\\
g) = {x^2}\left( {{x^6} - 64} \right)\\
 = {x^2}\left( {{x^3} - 8} \right)\left( {{x^3} + 8} \right)\\
 = {x^2}\left( {x - 2} \right)\left( {{x^2} + 2x + 4} \right)\left( {x + 2} \right)\left( {{x^2} - 2x + 4} \right)\\
h)\, = {x^{12}} - 2{x^6}{y^6} - {x^6}{y^6} + 2{y^{12}}\\
 = {x^6}\left( {{x^6} - 2{y^6}} \right) - {y^6}\left( {{x^6} - 2{y^6}} \right)\\
 = \left( {{x^6} - 2{y^6}} \right)\left( {{x^6} - {y^6}} \right)\\
 = \left( {{x^6} - 2{y^6}} \right){x^2}\left( {x - 2} \right)\left( {{x^2} + 2x + 4} \right)\left( {x + 2} \right)\left( {{x^2} - 2x + 4} \right)\\
i)\, = {\left( {{x^2} - 8} \right)^2} - {28^2}\\
 = \left( {{x^2} + 20} \right)\left( {{x^2} - 36} \right)\\
 = \left( {{x^2} + 20} \right)\left( {x - 6} \right)\left( {x + 6} \right)
\end{array}\)