Question

Which expression represents the volume of the box in terms of x?

Answer 1

`(40-2x)(32-2x)x`

Explanation:

Draw a rectangular cardboard, labelling the length 40 and the width 32

Now, draw in one of the 4 corners of the cardboard, a square box of length and width `x` inches. Repeat that with the other 3 corners of the cardboard.

Then if you look at the length of the cardboard, you will hopefully notice that there are `2x` in total when you add the length of the squares you drew in the corners. Since the cardboard is 40 inches and you cut out `2x` inches, then the length of your box is `40-2x`

Then if you look at the width of the cardboard, you will again notice that there are `2x` in total of the width of the squares you drew in the corners. Since the width of your cardboard is 32 inches and you cut out `2x` inches, then the width of your box is `32-2x`

![https://useruploads.socratic.org/prv5jicYTQC1YpajLhu3_box.png)

Above is a diagram for clarity.

Now to find the volume of your cardboard box, you would multiply the length by your breadth by your height ie `(40-2x)(32-2x)x`