Final answer:
The largest possible volume of the box is 0 cubic inches.
Step-by-step explanation:
The largest possible volume of a box with an open top and a square base can be found by maximizing the height of the box. To do this, we need to find the largest square that can be cut out from each corner of the cardboard. Since the side length of the cardboard is 40 inches, the side length of the square that can be cut out is 40 - 2x, where x is the length of the side of the square that is cut out. Therefore, the largest value for x is 20 inches. Therefore, the dimensions of the box will be 40 - 2(20) = 0 inches for the length and width, and 20 inches for the height.
To find the volume, we multiply the dimensions: 0 inches x 0 inches x 20 inches = 0 cubic inches.