A box without a top is made from a rectangular piece of cardboard, with dimensions 4 m by 2 m, by cutting out square corners with side length x. Which expression can be used to determine the greatest possible volume of the cardboard box?(x−4)(x−2)x(x−4)(x−2)x(4−2x)(2−2x)x(4x−2)(2x−4)

Answer:The expression that can be used to find the volume of the cardboard box is:(4−2x)(2−2x)xStep-by-step explanation:A box without a top is made from a rectangular piece of cardboard, with dimensions 4 m by 2 m, by cutting out square corners with side length x. i.e. the box is in the shape of a cuboid.Now the volume of a box is same as the volume of a cuboid.We know that the volume of a cuboid is given as:Volume of cuboid=Length×Breadth×Height.So, the length of the cuboid box is: 4-2xand the width of the box is: 2-2xAlso, the height of box is: xHence, the volume of cuboid is:[tex]Volume=(4-2x)\times (2-2x)\times x\\\\Volume=(4-2x)(2-2x)x[/tex]Hence, the expression for the volume of cuboid box is:              (4−2x)(2−2x)x