Cauchy Schwarz for 3 sequences of terms?

Question

I have something like this:

$(q^2+r^2)(s^2+t^2)(u^2+v^2)\geq(qsu+rtv)^2$

Assuming q, r, s, t, u and v are non-negative, I need to prove the inequality.

Is it simple enough as being able to state(or perhaps prove) that Cauchy Schwarz can extend for 3 sequences of terms(as opposed to two), or is this more of an algebraic manipulation sort of problem? I have a feeling it is more so the latter, but am not sure how to proceed.

Answer 1

$$LHS \ge ((qs)^2+ (rt)^2)(u^2+v^2) \ge RHS$$ by the CS inequality.