## Precalculus (6th Edition) Blitzer

The volume of the package in terms of the length of a side of its square front $x$ is, $V=108{{x}^{2}}-4{{x}^{3}}\text{ cubic inches}$.
Consider the length plus girth of provided package: $\text{108 inches}$ Now, the measurement of the length plus girth is the sum of the distance around that package and the longest side of girth $4x+y=108$ Or $y=10-8-4x$ The volume of provided package, $V=l\cdot w\cdot h$ Substitute $y$ for $l$ , and $x$ for $w$ and $h$ in the above equation \begin{align} & V=y\cdot x\cdot x \\ & =y\cdot {{x}^{2}} \end{align} Substitute $108-4x$ for $y$ in the above equation $V=\left( 108-4x \right)\cdot {{x}^{2}}$ Or $V=108{{x}^{2}}-4{{x}^{3}}$ The required volume of the package in terms of the length of a side of its square front $x$ is, $V=108{{x}^{2}}-4{{x}^{3}}\text{ cubic inches}$.