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

For a regular cube:
side length = $s[tex] volume = [tex]s^3$

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)
$s^3=s^2\times\s=(25a^2+40ab+16b^2)(5a+4b)$
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 = $\boxed{125a^3+300a^2b+240ab^2+64b^3}$

Answer 2

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