Question

QUESTION 4

An open-top box is formed by cutting squares out of a 3 inch by 5 inch piece of
paper and then folding up the sides. 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) = G-2x)5-2x)(x) Rewrite this equation by
expanding the polynomia

Answer 1

Explanation:

To expand the polynomial expression V(x) = (5 - 2x)(3 - 2x)(x), you can use the distributive property and multiply the terms. Here's the expanded expression:

V(x) = (5 - 2x)(3 - 2x)(x)

First, let's multiply the two binomials (5 - 2x) and (3 - 2x):

(5 - 2x)(3 - 2x) = 5(3) - 2x(3) - 2x(5) + (2x)(2x)

= 15 - 6x - 10x + 4x^2

= 4x^2 - 16x + 15

Now, you have the product of the two binomials:

V(x) = (4x^2 - 16x + 15)(x)

To expand this further, multiply each term inside the parentheses by x:

V(x) = 4x^3 - 16x^2 + 15x

So, the expanded polynomial expression for V(x) is:

V(x) = 4x^3 - 16x^2 + 15x