Answer
The expression for the volume of the box V made by cutting the squares from each corner of the square cardboard having sides equal to $24\text{ inches}$ is $V\left( x \right)=576x+4{{x}^{3}}-96{{x}^{2}}$.
The maximum volume is 1024 cubic inch and the length of the side of the square that should be cut from each corner is 4 inches.
Work Step by Step
See the graph below:
