Question

a cookie company packages its cookies in a rectangular prism box designed with square bases which have both a length and a width of 4 inches less than the height of the box. write a polynomial expression that represents the volume of a box with height x inches

Answer 1

Represent your unknowns:  Let s be the length of one side of the box.  The relationship between s and x is s = x-4.

The volume of the box is (length)(width)(height), which here equals the following:  V(x) = (x-4)*(x-4)*(x).  You may either leave this result as is, or shorten it to V(x) = (x-4)^2*x, or expand (x-4)*(x-4)*(x).

Answer 2

Answer: Our required expression for volume of a box is $x(x-4)^2$

Step-by-step explanation:

Let the height of the box be 'x'.

Let the length of the box be 'x-4'.

Let the width of the box be 'x-4'.

As we know the formula for volume of a box.

So, the volume of a box is given by

$Volume=Length\times Width\times Height\\\\Volume=(x-4)\times (x-4)\times x\\\\Volume=x(x-4)^2$

Hence, our required expression for volume of a box is $x(x-4)^2$