Answer:
[tex]V=80x-36x^2+4x^3[/tex]
Step-by-step explanation:
The volume of a box of dimensions a, b, c is:
V=abc
The box shown in the image has dimensions 8-2x, 10-2x, x, thus its volume is:
[tex]V=(8-2x)(10-2x)(x)[/tex]
Operating the first two brackets:
[tex]V=(80-16x-20x+4x^2)(x)[/tex]
Joining like terms:
[tex]V=(80-36x+4x^2)(x)[/tex]
Multiplying again:
[tex]V=80x-36x^2+4x^3[/tex]
The volume of the box is
[tex]\boxed{V=80x-36x^2+4x^3}[/tex]
