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 volume of the cube would be S^3, where S is the length of the side.

Volume = (5a + 4b)^3

Which becomes:

(5a+4b)(5a+4b)(5a+4b)  

Multiply the first two sets of parenthesis by each other:

(25a^2+40ab+16b^2)(5a+4b)  

Now multiply that by the 3rd set of parenthesis to get:

125a^3+300a^2b + 240ab^2 + b^3