SOLUTION: Given a square piece of material 25 inches on each side, we are to make an open box by cutting a square with x inches on a side from each corner and turning up the sides. Express t

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Question 121886: Given a square piece of material 25 inches on each side, we are to make an open box by cutting a square with x inches on a side from each corner and turning up the sides. Express the volumn V of the box in a function of x.

Answer by solver91311(12126) About Me  (Show Source):
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If you cut a square of side x from the corners of a 25 by 25 sheet, the length of each side of the bottom of the box will be 25 - 2x. The volume of a rectangular solid is V=lwh, here l = 25 - 2x, w = 25 - 2x, and h = x, so:

V=%2825-2x%29%2825-2x%29x

Using FOIL:
V=%28625-50x-50x%2B4x%5E2%29x

Distribute the x and collect terms:
V=4x%5E3-100x%5E2%2B625x