Final answer:
The volume of the rectangular prism with dimensions (x+2), (x-4), and (2x+1) is calculated as 2x^3 - 3x^2 - 18x - 8 cubic units.
Step-by-step explanation:
To find the volume of the rectangular prism with the given algebraic expressions for length, width, and height, we simply need to multiply these expressions together. The formula for the volume (V) of a rectangular prism is V = length × width × height. In this case, we are given:
- Length (l) = x + 2
- Width (w) = x - 4
- Height (h) = 2x + 1
Now let's calculate the volume:
V = (x + 2) × (x - 4) × (2x + 1)
To find the specific volume, we need to multiply these expressions:
First, multiply the length and width to get the area of the base:
Base area (A) = (x + 2)(x - 4) = x2 - 4x + 2x - 8 = x2 - 2x - 8
Then, multiply the base area by the height to get the volume:
V = (x2 - 2x - 8)(2x + 1) = 2x3 + x2 - 4x2 - 2x - 16x - 8
Simplify the expression:
V = 2x3 - 3x2 - 18x - 8
The volume of the rectangular prism with dimensions (x+2), (x-4), and (2x+1) is 2x3 - 3x2 - 18x - 8 cubic units.