2(p+3q)(p+2q)-(p+2q)^2-(3q+p)^2=2(p^2+2qp+3qp+6q^2)-p^2-4pq-4q^2-9q^2-6qp-p^2=2p^2+4qp+6qp+12q^2-p^2-4qp-4q^2-9q^2-6qp-p^2=-q^2
2(p+3q)(p+2q)-(p+2q)^2-(3q+p)^2=2(p^2+2qp+3qp+6q^2)-p^2-4pq-4q^2-9q^2-6qp-p^2=2p^2+4qp+6qp+12q^2-p^2-4qp-4q^2-9q^2-6qp-p^2=-q^2