We have been given the dimensions of the rectangular prism.
Lets say that the length, width, and height of the rectangular prism are:
Length [tex]= x+1[/tex]
Width [tex]=x-1[/tex]
Height[tex]=x[/tex]
Volume of a rectangular prism is given by:
[tex]length \times width\times height[/tex]
Plugging the values of length, width, and height, we get:
Total volume of the prism [tex]= (x+1)\times(x-1)\times x[/tex]
[tex]=(x^2-1)x=x^3-x[/tex] (we have used [tex](a+b)\times (a-b)=a^2-b^2[/tex])
So, the expression for the total volume of the prism is:
[tex](x^3-x)[/tex]
