$\begin{array}{l}
a)\,\,\,{\left( {x + y} \right)^3} - {x^3} - {y^3}\\
\,\,\,\,\,\, = {x^3} + 3{x^2}y + 3x{y^2} + {y^3} - {x^3} - {y^3}\\
\,\,\,\,\,\, = \,3{x^2}y + 3x{y^2} = 3xy(x + y)\\
b)\,{x^5} - 5{x^3} + 4x\\
\,\,\,\,\, = x\left( {{x^4} - 5{x^2} + 4} \right) = x\left( {{x^4} - 4{x^2} - {x^2} + 4} \right)\\
\,\,\,\, = \,x\left[ {{x^2}\left( {{x^2} - 4} \right) - \left( {{x^2} - 4} \right)} \right] = x\left( {{x^2} - 1} \right)\left( {{x^2} - 4} \right)\\
\,\,\,\,\, = x(x - 1)(x + 1)(x - 2)(x + 2)\\
c)\,\,{x^3} - 11{x^2} + 30x\\
\,\,\,\,\, = \,\,x\left( {{x^2} - 11x + 30} \right) = x\left( {{x^2} - 5x - 6x + 30} \right)\\
\,\,\,\,\, = x\left[ {x(x - 5) - 6(x - 5)} \right]\\
\,\,\,\,\, = x(x - 5)(x - 6)
\end{array}$
