1. The problem asks for the expression representing the total volume of a box with dimensions given by the expressions $(x + 2)$, $(2x - 1)$, and $(3x + 1)$. The volume of a box is found by multiplying its length, width, and height. 2. The formula for volume $V$ is: $$V = \text{length} \times \text{width} \times \text{height}$$ Here, that means: $$V = (x + 2)(2x - 1)(3x + 1)$$ 3. First, multiply the first two binomials: $$(x + 2)(2x - 1) = x \times 2x + x \times (-1) + 2 \times 2x + 2 \times (-1) = 2x^2 - x + 4x - 2 = 2x^2 + 3x - 2$$ 4. Now multiply this result by the third binomial $(3x + 1)$: $$ (2x^2 + 3x - 2)(3x + 1) = 2x^2 \times 3x + 2x^2 \times 1 + 3x \times 3x + 3x \times 1 - 2 \times 3x - 2 \times 1 $$ $$= 6x^3 + 2x^2 + 9x^2 + 3x - 6x - 2$$ 5. Combine like terms: $$6x^3 + (2x^2 + 9x^2) + (3x - 6x) - 2 = 6x^3 + 11x^2 - 3x - 2$$ 6. Therefore, the expression representing the total volume of the box is: $$\boxed{6x^3 + 11x^2 - 3x - 2}$$ This matches the second option given in the problem.