#### Answer

The length of the box on the right is represented by $10-2x$. Its width is represented by $10-2x$ . Its height is represented by $10-2x$. The volume of the box $V\left( x \right)$ in cubic inches is given by $V\left( x \right)=\left( 10-2x \right)\cdot \left( 10-2x \right)\cdot x$.

#### Work Step by Step

Consider the statement:
$\begin{align}
& \text{Length of the square}=15\ \text{inches} \\
& \text{Breadth of the square}=8\ \text{inches}
\end{align}$
A machine cuts equal sized squares from each corner, $x$, in inches such that the length and the breadth of the rectangle becomes:
$\begin{align}
& \text{Length of the square after cutting square, }x\text{, in inches}=10-x-x \\
& =10-2x\text{ }
\end{align}$
And
$\begin{align}
& \text{Breadth of the square after cutting square, }x\text{, in inches}=10-x-x \\
& =10-2x\text{ }
\end{align}$
And then the metal is shaped into an open box by turning up the sides.
So,
$\text{Height of the metal box}=x$
Use the formula:
$\text{Volume of the cube}=S\cdot S\cdot S$
Now, the expression for volume (V) of a cube is given by:
$V=\left( 10-2x \right)\cdot \left( 10-2x \right)\cdot \left( x \right)$