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)`