SOLUTION: I need some help on one of my math questions, I've included a picture of the diagram below Consider the following open-top box layout with cuts (solid lines) and folds (dotted l

Question 158127: I need some help on one of my math questions, I've included a picture of the diagram below
Consider the following open-top box layout with cuts (solid lines) and folds (dotted lines as indicated. The box is made by cutting out the corners but leaving sufficient material as flaps for gluing or tucking in.
http://picasaweb.google.com/swede5670/Math#5248354434228399282
Express the volume V of the resulting box as a function of the length of the corner cutout, X
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
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

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