An Open Box Is to Be Made from a Square $x ^ { 2 }$

Multiple Choice

An open box is to be made from a square piece of cardboard having dimensions 32 inches by 32 inches by cutting out squares of area $x ^ { 2 }$ from each corner as shown in the figure below. Express the volume V of the box as a function of x. $$32 - 2 x$$ $$32 - 2 x$$

A) $V ( x ) = 32 x ^ { 2 } - 2 x ^ { 3 }$
B) $V ( x ) = 32 x - 64 x ^ { 2 } + 4 x ^ { 3 }$
C) $V ( x ) = 1024 - 128 x + 4 x ^ { 2 }$
D) $V ( x ) = 1024 x - 128 x ^ { 2 } + 4 x ^ { 3 }$
E) $V ( x ) = 1024 x - 64 x ^ { 2 } + 4 x ^ { 3 }$