1. A rectangular piece of cardboard can be turned into an open box by cutting away identical squares from each corner and folding up the resulting flaps. The cardboard is 12 inches long and 12 inches

1. A rectangular piece of cardboard can be turned into an open box by cutting away identical squares from each corner and folding up the resulting flaps. The cardboard is 12 inches long and 12 inches wide.

a) Write an expression for the length of the box in terms of x (the length of each square you cut away).

b) Write an expression for the width of the box in terms of x.

c) Write an expression for the Volume of the box in terms of x.

d) Find the dimensions of the box that will yield the maximum volume.