Step 1 :The problem involves a rectangular sheet of cardboard measuring 24 inches by 38 inches. Corners are cut from this sheet to form a box.
Step 2 :The volume of a box is calculated by multiplying its length, width, and height. In this case, the length and width of the box are reduced by twice the height (since a square of side length \(h\) is cut from each corner of the cardboard), and the height of the box is \(h\).
Step 3 :Therefore, the volume of the box can be expressed as a function of \(h\) as follows: \(V(h) = (24-2h)(38-2h)h\).
Step 4 :Expanding this equation, we get the expanded form of the cubic function as \(V(h) = 4h^3 - 124h^2 + 912h\).
Step 5 :\(\boxed{V(h) = 4h^3 - 124h^2 + 912h}\) is the final answer.