Question

A manufacturer of shipping boxes has a box shaped like a cube. The side length is
(5a + 4b). What is the volume of the box in terms of a and b?

Answer 1

The vol. of a cube of side length s is V=s^3.

So, if the side length is 5a+4b, then the volume of the cube is

V(a, b) = (5a+4b)^3.  This could, of course, be expanded, using the binomial theorem, but there's no point in doing so.