There is a reason we call algebra expression x2 the “square.” Algebra formulas were fist derived from geometric pictures. The first page is a handout I usually give in an algebra class. showing how an algebra formula using squares can be understood geometrically as a dissection of a square, and on one with cube can be understood as the dissection of a cube. Of course this can be done for hypercubes and a 4th degree formula. Here is a picture by Justin Baker and Jeremy Kahn showing the geometric basis of the formula.
