Question

An open-top box is formed by cutting squares out of an 11 inch by 17 inch piece of

Answer 1

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

$V(x)=(17-2x)(11-2x)(x)$

To find:

The above equation by expanding the  polynomial.

Solution:

We have,

$V(x)=(17-2x)(11-2x)(x)$

Using distributive property, we get

$V(x)=[17(11-2x)-2x(11-2x)](x)$

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

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

Combining likes terms, we get

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

Using distributive property, we get

$V(x)=187x-56x^2+4x^3$

$V(x)=4x^3-56x^2+187x$

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