a rectangular piece of cardboard that measures 4 by 3 inches is to be formed into a rectangular box by cutting squares with length x from each corner and folding up sides. Find the volumes of the box in terms of x

To find the volume of the box in terms of x, we need to determine the dimensions of the box after cutting squares from each corner and folding up the sides.

Given that the original dimensions of the cardboard are 4 by 3 inches, if we cut squares with length x from each corner, the length of each side of the resulting box will be reduced by 2x.

The length of the box will be (4 - 2x) inches, and the width will be (3 - 2x) inches. The height of the box will be x inches.

Therefore, the volume of the box is given by the formula:

Volume = Length × Width × Height

Volume = (4 - 2x) × (3 - 2x) × x

Expanding the expression:

Volume = 4(3 - 2x)x - 2x(3 - 2x)x

Volume = 12x - 8x^2 - 6x^2 + 4x^3

Volume = 4x^3 - 14x^2 + 12x

So, the volume of the box in terms of x is given by the expression 4x^3 - 14x^2 + 12x.

4=2h+length

3=2h+width

but x has to be h
Volume=hwl=x(4-2x)(3-2x)

check that.