Question

A rectangular prism has dimensions of x + 1, x - 1, and x. Write an expression for the total volume of the prism.

Answer 1

We have been given the dimensions of the rectangular prism.

Lets say that the length, width, and height of the rectangular prism are:

Length $= x+1$

Width $=x-1$

Height$=x$

Volume of a rectangular prism is given by:

$length \times width\times height$

Plugging the values of length, width, and height, we get:

Total volume of the prism $= (x+1)\times(x-1)\times x$

$=(x^2-1)x=x^3-x$   (we have used $(a+b)\times (a-b)=a^2-b^2$)

So, the expression for the total volume of the prism is:

$(x^3-x)$