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

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.

Answer 2

A. a^3 + 3a^2b + 3ab^2 + b^3
B.125a^3 + 300a^2b + 240ab^2 + 64b^3
C.125a^3 - 300a^2b +240ab^2 - 64b^3
D.a^3 - 3a^2b + 3ab^2 - b^3

Answer 3

V=side*side*side
V=(5a+4b)(5a+4b)(5a+4b)
V=(25a^2+40ab+16b^2)(5a+4b)
V=125a^3+300a^2b + 240ab^2 + b^3

Answer 4

B.