If $\alpha, \beta, \gamma, \delta$ be the roots of the equation $x^4+px^3+qx^2+rx+s=0$, Show that the equation whose roots are $(\alpha \beta + \gamma \delta), (\beta \gamma + \alpha \delta), (\gamma \alpha + \beta \delta)$ is $$x^3-qx^2+(pr-4s)x-(r^2-4qs+p^2s)=0$$
I'm really stuck on this one. I've tried using simple manipulations, methods for finding equations with symmetric functions of roots, Newton's theorem. But, nothing seems to work. Any kind of help is appreciated.