Answer: V = (12in - 2*x)*(8 in - 2*x)*x
Step-by-step explanation:
So we have a rectangular cardboard sheet, and we cut four squares of side length x in each corner so we can make a box.
Remember that for a box of length L, width W and height H, the volume is:
V = L*W*H
In this case, the length initially is 12 inches, but we remove (from each end) x inches of the length, then the length of the box will be:
L = 12 in - 2*x
For the width we have a similar case:
W = 8in - 2*x
And te height of the box will be equal to x, then:
H = x
This means that the volume is:
V = (12in - 2*x)*(8 in - 2*x)*x
Here we can see the connection between the cutout and the volume of the box
