(m-2n-p)(m-2n+p)-(m+2n+p)(m+2n+p)
=[(m-2n)-p][(m-2n)+p]-[(m+2n)+p][(m+2n) +p]
=(m-2n)^2-p^2-(m+2n)^2-2(m+2n)p-p^2
=-8mn-2(m+2n)p-2p^2
=-8mn-2mp-4np-2p^2
=-2(p+m)(p+2n)-4mn
(m-2n-p)(m-2n+p)-(m+2n+p)(m+2n+p)
=[(m-2n)-p][(m-2n)+p]-[(m+2n)+p][(m+2n) +p]
=(m-2n)^2-p^2-(m+2n)^2-2(m+2n)p-p^2
=-8mn-2(m+2n)p-2p^2
=-8mn-2mp-4np-2p^2
=-2(p+m)(p+2n)-4mn