An open-top box is formed by cutting squares out of an 11 inch by 17 inch piece of
paper and then folding up the sides. The volume V(2) in cubic inches of this type of
open-top box is a function of the side length x in inches of the square cutouts and can
be given by V(x) = (17 – 2x)(11 – 2x)(x). Rewrite this equation by expanding the
polynomial.

Question

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Respuesta :

erinna erinna · Answer 1 · 2020-09-20T02:59:01+02:00

Given:

The volume V(x) in cubic inches of this type of open-top box is a function of the side length x in inches of the square cutouts and can be given by

[tex]V(x)=(17-2x)(11-2x)(x)[/tex]

To find:

The above equation by expanding the polynomial.

Solution:

We have,

[tex]V(x)=(17-2x)(11-2x)(x)[/tex]

Using distributive property, we get

[tex]V(x)=[17(11-2x)-2x(11-2x)](x)[/tex]

[tex]V(x)=[17(11)+17(-2x)-2x(11)-2x(-2x)](x)[/tex]

[tex]V(x)=[187-34x-22x+4x^2](x)[/tex]

Combining likes terms, we get

[tex]V(x)=[187-56x+4x^2](x)[/tex]

Using distributive property, we get

[tex]V(x)=187x-56x^2+4x^3[/tex]

[tex]V(x)=4x^3-56x^2+187x[/tex]

Therefore, the required equation after expanding the polynomial is [tex]V(x)=4x^3-56x^2+187x[/tex].