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? Show your work.

Answer 1

Volume of a square = (s)(s)(s) and s=5a+4b Therefore: (5a+4b)(5a+4b)(5a+4b)= (25a^2+40ab+16b^2)(5a+4b)= (125a^3+200a^2b+80ab^2+100a^2b+160ab^2+64b^3)= (125a^3+300a^2b+240ab^2+64b^3) You just multiple the first time the second and then do so again with the combination of the first two times the second. A little cleaning up and you are left with an equation in terms of a and b.