Question 22529
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