Systems of Equations · Challenge problem

For every pair of numbers $x$ and $y$ with $x + y = s$ and $xy = p$, express each of the following in terms of $s$ and $p$ alone.

$(a)\ x^3 + y^3$ $(b)\ (x-y)^2$ $(c)\ \dfrac{x}{y} + \dfrac{y}{x}$