$\begin{array}{l}
a)\,\,\,{\left( {3x + 1} \right)^3} = 27{x^3} + 27{x^2} + 3x + 1.\\
b)\,\,\,{\left( {\frac{x}{3} - 1} \right)^3} = \frac{{{x^3}}}{{27}} - \frac{{{x^2}}}{9} + x - 1.\\
c)\,\,{\left( { - {y^2} + 3x} \right)^3} = {\left( {3x - {y^2}} \right)^3} = 27{x^3} - 27{x^2}{y^2} + 9x{y^4} - {y^4}\\
d)\,\,{\left( {\frac{x}{y} - \frac{{2y}}{x}} \right)^3} = {\left( {\frac{x}{y}} \right)^3} - 3{\left( {\frac{x}{y}} \right)^2}\frac{{2y}}{x} + 12\frac{x}{y}.{\left( {\frac{y}{x}} \right)^2} - \frac{{8{y^3}}}{{{x^3}}}\\
= \frac{{{x^3}}}{{{y^3}}} - \frac{{6x}}{y} + \frac{{12y}}{x} - \frac{{8{y^3}}}{{{x^3}}}.
\end{array}$
