a) (x – y)(x$^{2}$ + xy + y$^{2}$) = x$^{3}$ + x$^{2}$y + xy$^{2}$ - x$^{2}$y - xy$^{2}$ - y$^{3}$ = x$^{3}$ - y$^{3}$;
b) (x$^{2}$ - 2xy + y$^{2}$)(x – y) = x$^{3}$ - 2x$^{2}$y + xy$^{2}$ - x$^{2}$y + 2xy$^{2}$ - y$^{3}$ = x$^{3}$ - 3x$^{2}$y + 3xy$^{2}$ - y$^{3}$;
c) (x$^{2}$y$^{2}$ - $\frac{1}{3}$xy + 3y)(x – 3y) = x$^{3}$y$^{2}$ - $\frac{1}{3}$x$^{2}$y + 3xy – 3x$^{2}$y$^{3}$ + xy$^{2}$ - 9y$^{2}$;
d) ($\frac{1}{5}$x – 1)(x$^{2}$ - 5x + 2) = $\frac{1}{5}$x$^{3}$ - x$^{2}$ + $\frac{2}{5}$x - x$^{2}$ + 5x – 2 = $\frac{1}{5}$x$^{3}$ - 2x$^{2}$ + $\frac{27}{5}$x - 2.