Question

Write an expression for the volume of a rectangularprism if the length is 25 cm shorter than some given amount, x, and the width is 14 cm longer than x and the height is x cm.

Answer 1

The volume of a prism is given by:

$V=lwh$

We know that the height is x. The length is 25 shorter than x, this can be express as:

$x-25$

The width is 14 longer than x, this can be express as:

$x+14$

Plugging the expressions for the length, the width and the height we have that:

$\begin{gathered} V=(x-25)(x+14)x \\ V=x(x-25)(x+14) \end{gathered}$

Therefore, the volume of the prism is:

$V=x(x-25)(x+14)$