A rectangular box with a square base is 20 inches wider than it is tall. If x represents the width of the base of the box, then the volume of the box as a function of x is? ...
please help me with this problem
The volume of a rectangular prism is length * width * height.
$\displaystyle V = lwh$
You're given that the width is x.
Since the prism has a square base, the length is also x.
If the box is "20 inches wider than it is tall," then the height is the width minus 20 inches, or height = x - 20.
Put it all together you get
$\displaystyle \begin{aligned}
V &= lwh \\
&= x \cdot x \cdot (x - 20) \\
&= x^2(x - 20) \\
\end{aligned}$