What is the volume of a rectangular prism if the length is #(4x)#, the width is #(x+1)#, and the height is #(2x-1)#?

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Answer 1 · 2018-04-07T02:09:58

#v=8x^3+4x^2-4x#

The volume of a rectangular prism is given by

#V=lwh# where #l, w, h# represent length, width, and height, respectively.

We're given #l=4x, w=x+1, h=2x-1#

Thus,

#v=4x(x+1)(2x-1)#

We need to multiply this out. First, we should multiply the two binomials, #(x+1)(2x-1)#

#v=4x(2x^2-x+2x-1)#

Combine like terms.

#v=4x(2x^2+x-1)#

Distribute the #4x.# Recall that #x^ax^b=x^(a+b)#.

#v=(4)(2)(x^2)(x)+4(x)(x)-4x#

#v=8x^3+4x^2-4x#