Janelle is using a piece of cardstock to create an open box with no top. The cardstock is 8 inches by 11 inches. She cuts a square with length out of each corner and folds up the sides to create the box. Find the volume of the box, , in standard form.

Since Janelle cuts a square of side length x out of each corner of the cardstock, we have a length x + x = 2x cut out of each dimension of the cardstock.

Since the dimensions of the cardstock are 8 inches by 11 inches, cutting out a length of 2x inches from each dimension to produce the length, L and width, w of the open box, we have the length of the open box, L = 8 -2x and the width of the open box, W = 11 - 2x.

Since the height of the open box is the length x of the square cut out of each corner, and the open box is a rectangular box,

So, the volume of the box is

V = LWx

Substituting the values of the variables into the equation, we have

V = LWx

V = (8 - 2x)(11 - 2x)x

Expanding the brackets, we have

V = (88 - 16x - 22x + 4x²)x

V = (88 - 38x + 4x²)x

V = 88x - 38x² + 4x³

Re-arranging, we have

V = 4x³ - 38x² + 88x

So, the volume of the box in standard form is 4x³ - 38x² + 88x

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