SOLUTION: The width and height of a rectangular carton are the same. The length is one foot longer than the height. The carton is then placed inside a second carton in the shape of a cube wi

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: The width and height of a rectangular carton are the same. The length is one foot longer than the height. The carton is then placed inside a second carton in the shape of a cube wi      Log On


   

Question 22529: The width and height of a rectangular carton are the same. The length is one foot longer than the height. The carton is then placed inside a second carton in the shape of a cube with the same length as the first carton. Write a polynomial expression for the space that remains inside the second carton.
Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
LET WIDTH = HEIGHT =X FOR THE RECTANGULAR CARTON.
LENGTH = 1 FT.LONGER = X+1
VOLUME OF THIS CARTON = X*X*(X+1)=X^3+X^2
LENGTH OS SECOND CARTON = SAME AS LENGTH OF ABOVE CARTON = X+1=HEIGHT = WIDTH..SINCE IT IS A CUBE.
VOLUME OF CUBE =(X+1)(X+1)(X+1)=X^3+3X^2+3X+1
HENCE SPACE LEFT OVER =
=X^3+3X^2+3X+1-(X^3+X^2)=2X^2+3X+1