An open-top box is constructed from a 12-inch square piece of cardboard by cutting an equal x-inch square from each corner and folding up the sides. Which polynomial represents the volume of the box in cubic inches?
Ax(12 − 2x)²
Bx(12 − x)²
C12x − 4x²
D144 − 4x²
Explanation
After cutting an x-inch square from each corner, the base of the box becomes (12 − 2x) by (12 − 2x), and the height is x. So V = x(12 − 2x)(12 − 2x) = x(12 − 2x)². Choice B forgets that x is removed from BOTH ends of each side. C and D drop the height factor.
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