Question

Find volume of rectangular prism length(4x+3) width (x-6) height (2x-1)

Answer 1

8x^3-46x^2-5x+18

Explanation:

The volume of a rectangular prism is L*W*H where

L=length

W=width

H=height.

So we want to probably find the standard form of this multiplication because writing (4x+3)(x-6)(2x-1) is too easy.

Let's multiply (4x+3) and (x-6), then take that result and multiply it to (2x-1).

(4x+3)(x-6)

I'm going to use FOIL here.

First: 4x(x)=4x^2

Outer: 4x(-6)=-24x

Inner: 3(x)=3x

Last: 3(-6)=-18

---------------------------Add.

4x^2-21x-18

So we now have to multiply (4x^2-21x-18) and (2x-1).

We will not be able to use FOIL here because we are not doing a binomial times a binomial.

We can still use distributive property though.

(4x^2-21x-18)(2x-1)

=

4x^2(2x-1)-21x(2x-1)-18(2x-1)

=

8x^3-4x^2-42x^2+21x-36x+18

Now the like terms are actually already paired up we just need to combine them:

8x^3-46x^2-5x+18

Answer 2

`\large\boxed{8x^3-46x^2-15x+18}`

Explanation:

The formula of a volume of a rectangular prism:

`V=lwh`

l - length

w - width

h - height

We have l = 4x + 3, w = x - 6 and h = 2x - 1.

Substitute:

`V=(4x+3)(x-6)(2x-1)`

use FOIL: (a + b)(c + d)

`V=\bigg[(4x)(x)+(4x)(-6)+(3)(x)+(3)(-6)\bigg](2x-1)\\\\=(4x^2-24x+3x-18)(2x-1)\qquad\text{combine like terms}\\\\=(4x^2-21x-18)(2x-1)`

use the distributive property: a(b + c) = ab + ac

`V=(4x^2-21x-18)(2x)+(4x^2-21x-18)(-1)\\\\=(4x^2)(2x)+(-21x)(2x)+(-18)(2x)+(4x^2)(-1)+(-21x)(-1)+(-18)(-1)\\\\=8x^3-42x^2-36x-4x^2+21x+18`

combine like terms

`V=8x^3+(-42x^2-4x^2)+(-36x+21x)+18\\\\=8x^3-46x^2-15x+18`