\(a)\) \(5x - 5y + ax – ay\)
\( = \left( {5x - 5y} \right) + \left( {ax - ay} \right)\)
\( = 5\left( {x - y} \right) + a\left( {x - y} \right) \)
\(= \left( {x - y} \right)\left( {5 + a} \right)\)
\(b)\) \({a^3} - {a^2}x - ay + xy\)
\( = \left( {{a^3} - {a^2}x} \right) - \left( {ay - xy} \right)\)
\( = {a^2}\left( {a - x} \right) - y\left( {a - x} \right)\)
\( = \left( {a - x} \right)\left( {{a^2} - y} \right)\)
\(c)\) \(xy\left( {x + y} \right) + yz\left( {y + z} \right) + xz\left( {x + z} \right)\)\( + 2xyz\)
\(= {x^2}y + x{y^2} + yz\left( {y + z} \right) + {x^2}z + x{z^2}\)\( + xyz + xyz \)
\(= \left( {{x^2}y + {x^2}z} \right) + yz\left( {y + z} \right) \)\( + \left( {x{y^2} + xyz} \right)+ \left( {x{z^2} + xyz} \right) \)
\(= {x^2}\left( {y + z} \right) + yz\left( {y + z} \right) \)\(+ xy\left( {y + z} \right) + xz\left( {y + z} \right) \)
\(= \left( {y + z} \right)\left( {{x^2} + yz + xy + xz} \right)\)
\( = \left( {y + z} \right)\left[ {\left( {{x^2} + xy} \right) + \left( {xz + yz} \right)} \right] \)
\( = \left( {y + z} \right)\left[ {x\left( {x + y} \right) + z\left( {x + y} \right)} \right]\)
\( = \left( {y + z} \right)\left( {x + y} \right)\left( {x + z} \right) \)
