Design an equation for the volume of a box made from a cardboard sheet of length q and width p and square cutouts of side length x.

Consider the figure.

From the cardboard sheet of length q and width p, we remove from the corners squares of side length x, then fold the cardboard to form a box.

the height of the box is x, the length is q-2x, since 2 x'es are subtracted from the length of the cardboard, similarly the width of the box is p-2x.

The volume of the box is height*length*width:

so the equation is

V=x (q-2x) (p-2x)