Question

Find an expression for the volume of a rectangular prism with a length of (x + 5), width of (x - 4) and a height of (x-7)

Answer 1

Given:

The length of a rectangular prism is (x + 5), the width is (x - 4), and (x - 7).

To find:

The expression for the volume of the rectangular prism.

Solution:

It is known that the volume of the rectangular prism is given by:

`V=l* w* h`

So, the volume of the given rectangular prism is:

`\begin{gathered} V=(x+5)(x-4)(x-7) \\ =(x^2+5x-4x-20)(x-7) \\ =(x^2+x-20)(x-7) \\ =x^3+x^2-20x-7x^2-7x+140 \\ =x^3-6x^2-27x+140 \end{gathered}`

Thus, the expression for the volume of the rectangular prism is x^3 - 6x^2 - 27x + 140.