I am a bit delayed ¡­

I am a bit delayed posting new problems. However, for problem IV.1.12 (the one I messed up during the seminar, sorry again for that), I will re-assign it: prove in detail the case n=2, and notice what identities you had to show for this case. Then use these identities for induction on P^n or Q^n. (Both ways work, actually.)