Chris M. answered • 12/11/17

Tutor

5
(18)
Patient and Effective Math Instructor with Decades of Experience

For problems like this I always start by making a sketch (tough to do on this forum).

I'd draw the original square, carving out the (x+1)by(x+1) corners. Then visualize folding the corners up into the rectangular prism (box).

So what are the dimensions for this box.

Length=18-(x+1)-(x+1)=18-2(x+1)=18-2x-2=16-2x=2(8-x)

Width=2(10-x) <-- Same as the length since we are starting with a cube

Height=x-1

The volume of the box is simply (Length)(Width)(Height)

Substituting our expressions for each of these dimensions we have

Volume=2(8-x)2(8-x)(x+1)

=4(64-16x+x

^{2})(x+1)=4(64x-16x

^{2}+x^{3}+64-16x+x^{2})=4(x

^{3}-15x^{2}+48x+64)=4x

^{3}-60x^{2}+192x+256Good Luck

Cheers

-Chris