SOLUTION: This is a challenge problem on my homework and I don't completely understand it. Would someone please help me? A box with a square bottom is to be made from a 12 inch square

Question 703484: This is a challenge problem on my homework and I don't completely understand it. Would someone please help me?

A box with a square bottom is to be made from a 12 inch square piece of cardboard. Squares with the side x are cut out of the corners, and the sides are folded up. Express the volume and the surface area of the outside of the box as polynomials.
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
This problem keeps coming up and I am always re-drawing the picture.

As you cut squares out of each corner (I made them red),
each square measuring inches to a side,
you get four -inch wide flaps to fold up around the (green) square bottom.
The side of that green square is inches long.
The surface area of the green square is square inches.
The flaps/sides will be inches by inches,
with a total surface area of square inches.
The surface area of the box (just four sides and bottom, because we have no top/lid) is
square inches, so

The box will be -inches high,
with a base surface of square inches (as calculated above),
and a volume of
-->

NOTE:
I know I make stupid arithmetic mistakes, so don't trust my calculations.
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