HELP URGENTLY NEEDED -- algebra, precalculus

Hello all, I've been struggling with the following problem:

We have $p,q,r,s,t$and  $u$ as nonnegative real numbers.
i. Show that $(p^2 + q^2)^2 (r^4 + s^4)(t^4 + u^4) ≥ (prt + qsu)^4.$
ii. Show that $(p^2 + q^2)(r^2 + s^2)(t^2 + u^2) ≥ (prt + qsu)^2.$

So far I have put $r^2, s^2, t^2$ and $u^2$ into the Cauchy-Schwarz form : $(r^4+s^4)(t^4+u^4)\geq(r^2t^2+s^2u^2)^2$; but after this I don't know how to continue. I also have no idea where to begin for part ii. Please help, I'm very confused!