It takes A algebra books (all the same thickness) and H geometry books (all the same thickness, which is greater than that of an algebra book) to completely fill a certain shelf. Also, S of the algebra books and M of the geometry books would fill the same shelf. Finally, E of the algebra books alone would fill this shelf. Given that A,H,S,M,E are distinct positive integers, it follows that E is<spanclass=′latex−bold′>(A)</span>M+HAM+SH<spanclass=′latex−bold′>(B)</span>M2+H2AM2+SH2<spanclass=′latex−bold′>(C)</span>M−HAH−SM<spanclass=′latex−bold′>(D)</span>M−HAM−SH<spanclass=′latex−bold′>(E)</span>M2−H2AM2−SH2