Question

Determine the volume of a cube that has a side length of (x+3). Draw a picture, label it, and write a simplified polynomial to represent the volume.

Answer 1

To find the volume of a cube whose sides are (x+3) in length, you cube the expression to obtain the volume V = (x+3)³, which can be expanded to V = x³ + 9x² + 27x + 27. This is the simplified polynomial that represents the volume of the cube.

Step-by-step explanation:

Calculating the Volume of a Cube with Side (x+3) To determine the volume of a cube with a side length of (x+3), we use the formula for the volume of a cube, which is V = s³, where 's' is the length of a side of the cube. In this scenario, the side length 's' is (x+3). Thus, to calculate the volume, we cube the side length:

Volume (V) = (x+3)³

Expanding the polynomial, we get:

Volume (V) = x³ + 9x² + 27x + 27

This simplified polynomial represents the volume of the cube.

While I cannot draw a picture here, imagine a cube with each side labeled as (x+3) to visualize the concept.