Answer :
You have to multiply the polynomials by each other:
(2x-1) * (5x-4) =10x^2-13x+4
(10x^2-13x+4)(x+4)=
10x^3+27x^2-48x+16
(2x-1) * (5x-4) =10x^2-13x+4
(10x^2-13x+4)(x+4)=
10x^3+27x^2-48x+16
Answer:
D. [tex]10x^3+27x^2-48x+16[/tex]
Step-by-step explanation:
We have been given lengths of a box as: [tex](2x-1),(5x-4)\text { and }(x+4)[/tex]. We are asked to find the volume of our given box.
Since all the sides of box are not equal, therefore, our box is a rectangular box.
Since the volume of a rectangular box equals the product of all of its sides, so we will multiply our given sides to find the volume of box as:
[tex](2x-1)(5x-4)(x+4)[/tex]
First of all we will multiply our first two expressions as:
[tex](2x-1)(5x-4)=2x*5x-2x*4-1*5x-1*-4[/tex]
[tex](2x-1)(5x-4)=10x^2-8x-5x+4[/tex]
[tex](2x-1)(5x-4)=10x^2-13x+4[/tex]
Now we will multiply [tex](10x^2-13x+4)[/tex] with [tex](x+4)[/tex].
[tex](10x^2-13x+4)(x+4)[/tex]
[tex]10x^2*x+10x^2*4-13x*x-13x*4+4*x+4*4[/tex]
[tex]10x^3+40x^2-13x^2-52x+4x+16[/tex]
[tex]10x^3+27x^2-48x+16[/tex]
Therefore, the volume of our given box is [tex]10x^3+27x^2-48x+16[/tex] cubic units and option D is the correct choice.