Question

A suitcase has a length that is 10 inches greater than its width. The sum of the length, width and height of the suitcase is 40 inches. Write a polynomial expression to represent V, the volume of a rectangular prism. (Volume = (length)(width)(height).

Answer 1

Solve the following for L, w and h:
{ L=w+10, L+w+h=40 }
{w -> -10 + L, h -> 50 - 2 L}

V = L w h
Replace w and h with -10 + L and 50 - 2 L respectively and simplify
V = (50 - 2 L) (-10 + L) L}

Expand to:\[ V=-2 L^3+70 L^2-500 L \]