The volume (in cubic feet) of a room is represented by 12z3−27z12z3−27z. find expressions that could represent the remaining dimensions of the room when the length (in feet) is represented by 2z−32z−3.

The volume of a room = length * width * height
                                    =12z³-27z
And by the analysis:
     The volume = 12z³-27z
                          = ( 3z ) ( 4z²-9 )              ⇒ by taking (3z) common
                          = ( 3z )( 2z+3 )( 2z-3 )    ⇒ the difference between two squares

So the dimensions of the room will be 3z , 2z+3 , 2z-3
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