To find the volume of the right rectangular prism, let's break down the problem step-by-step:
1. Understand the dimensions of the prism:
- The base of the prism is a square with an edge length of [tex]\( x \)[/tex] units.
- The height of the prism is 3 units greater than the length of the base, which means the height is [tex]\( x + 3 \)[/tex] units.
2. Volume formula:
The volume [tex]\( V \)[/tex] of a right rectangular prism is calculated by multiplying the length, width, and height of the prism:
[tex]\[
V = \text{length} \times \text{width} \times \text{height}
\][/tex]
3. Substitute the given dimensions:
- Length of the base = [tex]\( x \)[/tex] units
- Width of the base (since it's a square) = [tex]\( x \)[/tex] units
- Height of the prism = [tex]\( x + 3 \)[/tex] units
Substituting these values into the volume formula gives:
[tex]\[
V = x \times x \times (x + 3)
\][/tex]
4. Simplify the expression:
Multiply the terms:
[tex]\[
V = x \times x \times (x + 3) = x^2 \times (x + 3)
\][/tex]
Distribute [tex]\( x^2 \)[/tex] over the terms inside the parentheses:
[tex]\[
V = x^2 \cdot x + x^2 \cdot 3 = x^3 + 3x^2
\][/tex]
Therefore, the expression that represents the volume of the prism is:
[tex]\[
\boxed{x^3 + 3x^2}
\][/tex]
This matches the second option given in the list.
