Answer:
8x^3-46x^2-5x+18
Step-by-step 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:
[tex]\large\boxed{8x^3-46x^2-15x+18}[/tex]
Step-by-step explanation:
The formula of a volume of a rectangular prism:
[tex]V=lwh[/tex]
l - length
w - width
h - height
We have l = 4x + 3, w = x - 6 and h = 2x - 1.
Substitute:
[tex]V=(4x+3)(x-6)(2x-1)[/tex]
use FOIL: (a + b)(c + d)
[tex]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)[/tex]
use the distributive property: a(b + c) = ab + ac
[tex]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[/tex]
combine like terms
[tex]V=8x^3+(-42x^2-4x^2)+(-36x+21x)+18\\\\=8x^3-46x^2-15x+18[/tex]
