Precalculus

From a rectangular piece of cardboard having dimensions a × b, where a = 40 inches and b = 70 inches, an open box is to be made by cutting out an identical square of area x2 from each corner and turning up the sides (see the figure). Express the volume V of the box in terms of x. (Factor your answer completely.)

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  1. after turning up the corners, the bottom now measures

    (a-2x)(b-2x)

    The depth of the box is the size of the tabs folded up, or x

    V = (a-2x)(b-2x)(x)
    = x(40-2x)(70-2x)
    = 4x(20-x)(35-x)

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