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 work

Answer 1

the answer is (12x) -(20+8x)
`\geq` 100

12x-20-8x
`\geq`

4x-20
`\geq` 100

20 + 120

4x
`\geq` 120

4x
`\geq`120

x
`\geq`30

Answer 2

For a regular cube:
side length =
`image`

This problem has a lot of distributing. I suggest you use a grid to make sure each term is distributed (see attached image on how to do this)

For our problem:
side length =
`s=5a+4b`

`s^2=25a^2+40ab+16b^2` (use FOIL)

`s^3=s^2*\s=(25a^2+40ab+16b^2)(5a+4b)`
Multiplying 5a(25a²+40ab+16b²) =
`125a^3+200a^2b+80ab^2`
Multiplying 4b(25a²+40ab+16b²) =
`100a^2b+160ab^2+64b^3`
Combine like terms. (200a²b + 100a²b = 300a²b, 80ab² + 160ab² = 240ab²)

volume = s³ =
`\boxed{125a^3+300a^2b+240ab^2+64b^3}`