A box with an open top is to be constructed from a rectangular piece of cardboard with dimensions 12 in. by 20 in. by cutting out equal squares of side at each corner and then folding up the sides as in the figure. Express the volume V of the box as a function of x. 

Step 1:

The dimensions of the cardboard 12 in. by 20 in.

Observe the figure:

The height of the box = x in.

The width of the box = width of the cardboard - 2(x) = 12 - 2x.

The length of the box = length of the cardboard - 2(x= 20 - 2x.

Volume of the box = Length  Width  Height.
\ Step 2:

Volume of the box = 

From the above expression, the values of x are .
\

The volume of the box as a function of x is , .

Solution :

The volume of the box as a function of x is , .