1. **State the problem:** We need to find the simplified expression for the volume of a rectangular prism with dimensions $2x$, $x+2$, and $4x-1$. 2. **Formula for volume of a rectangular prism:** $$\text{Volume} = \text{length} \times \text{width} \times \text{height}$$ Here, the volume is: $$V = (2x)(x+2)(4x-1)$$ 3. **Step 1: Multiply the first two factors:** $$ (2x)(x+2) = 2x \times x + 2x \times 2 = 2x^2 + 4x $$ 4. **Step 2: Multiply the result by the third factor:** $$ (2x^2 + 4x)(4x - 1) $$ Use distributive property: $$ = 2x^2 \times 4x + 2x^2 \times (-1) + 4x \times 4x + 4x \times (-1) $$ $$ = 8x^3 - 2x^2 + 16x^2 - 4x $$ 5. **Step 3: Combine like terms:** $$ 8x^3 + ( -2x^2 + 16x^2 ) - 4x = 8x^3 + 14x^2 - 4x $$ 6. **Final answer:** $$\boxed{8x^3 + 14x^2 - 4x}$$ This is the simplified expression for the volume of the rectangular prism.