Proof

[full river]

(3r-1)^3 = 27r^3 - 27r^2 + 9r - 1
= 9(3r^3 - 3r^2 + r) -1

do the same for the other 2 cases

5a)(p+q)^2 >= 4pq
p^2 + q^2 + 2pq >= 4pq
p^2 + q^2 - 2pq >= 0
(p-q)^2 >= 0
(p-q)^2 >= 0 is always true and all these steps are reversable