Question

Help!

An open-top box is formed by cutting squares out of a 5 inch by 7 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)=(7–2x)(5-2x)(x).
Rewrite this equation by expanding the polynomial.

ENTER YOUR RESPONSE

Answer 1

Answer:

$V(x) = 4x^3 - 24x^2+35x$

Step-by-step explanation:

Given

$V(x) = (7 - 2x)(5 - 2x)(x)$

Required

Form a polynomial

We have that:

$V(x) = (7 - 2x)(5 - 2x)x$

This can be rewritten as

$V(x) = x * (7 - 2x)(5 - 2x)$

This gives:

$V(x) = (7x - 2x^2)(5 - 2x)$

Expand bracket

$V(x) = 7x(5 - 2x) - 2x^2(5 - 2x)$

$V(x) = 35x - 14x^2 - 10x^2 + 4x^3$

$V(x) = 35x - 24x^2 + 4x^3$

$V(x) = 4x^3 - 24x^2+35x$