Abox without a top is made from a rectangular piece of cardboard, with dimensions 12 cm by 10 cm, by cutting out square corners with side length x. which expression can be used to determine the greatest possible volume of the cardboard box?

The volume of this box can be given by 

V=(12-2x)(10-2x)(x), or in simplified form, V=120x-44x²+4x³.

To find the volume of the box, we would subtract x from both ends of the length, so 12-2x.  We also subtract x from both ends of the width, so 10-2x.  The height of the box is given by the x amount that is cut out from the box.  Volume of a box is given by length*width*height.