Question 158127
The original dimensions are: length is 40 inch and width is 20 inch
.
Once we cut the square (each side length x) at each corner the dimensions are (study your diagram):
length: 40 - 2x
width: 20 -2x
.
The volume of the box is length*width*depth.
The depth is x (from the diagram).
.
Therefore we have:
V = x(40-2x)(20-2x)
Applying FOIL:
V = x(800-80x-40x+4x^2)
V = x(800-120x+4x^2)
V = x(4x^2-120x+800)
V = 4x^3-120x^2+800x