Question 255962
To make an open box we can cut squares out of the corners and fold the sides up.  If x is the length of the side we are cutting then when we fold that side up, x will be the height (take a minute to think about what this looks like when you cut out the box length x and then fold that flap up. the x inch piece you cut is the amount you are folding up so that is the height.)

So x is the height.  We are looking for the volume so we will also need the length and width since the formula for volume is the product (*) of length, width and height.

We cut off x inches off the length and width on each side (again think about what this looks like). We are taking 2x off each measurement (one x from each end).  So now instead of a length of 8 inches, our length is 8-2x inches.
Similarly, our width of 10 inches was cut down by 2x also to give us 10-2x inches.

Now we have in terms of x the length, width and height.  The volume is the product of these three, so substitute them in.  Let V(x) be the volume.

V(x)=length* width *height= (8-2x)*(10-2x)*(x)

We'll simplify for fun- FOIL the first two
{{{V(x)=(80-20x-16x+4x^2)(x)}}}
{{{V(x)=(80-36x+4x^2)(x)}}}
Distribute x over each term
{{{V(x)=80x-36x^2+4x^3}}}

Note that the volume is going to be in cubic inches (inch*inch*inch)=(inch^3)