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

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1 Answer
Jun 9, 2018

(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