Differentiate the expression (x2 + 3)(2x2 - 1) with respect to x.

Let $y = (x^2 + 3)(2x^2 - 1)$.
Multiply the terms:

$$y = x^2(2x^2) + x^2(-1) + 3(2x^2) + 3(-1)$$ $$y = 2x^4 - x^2 + 6x^2 - 3$$

Combine like terms:

$$y = 2x^4 + 5x^2 - 3$$

We use the power rule for differentiation, which states that $\frac{d}{dx}(ax^n) = anx^{n-1}$, and the derivative of a constant is 0.

$$\frac{dy}{dx} = \frac{d}{dx}(2x^4) + \frac{d}{dx}(5x^2) - \frac{d}{dx}(3)$$

For $2x^4$:

$$\frac{d}{dx}(2x^4) = 2 \cdot 4x^{4-1} = 8x^3$$

For $5x^2$:

$$\frac{d}{dx}(5x^2) = 5 \cdot 2x^{2-1} = 10x$$

For $-3$:

$$\frac{d}{dx}(-3) = 0$$

$$\frac{dy}{dx} = 8x^3 + 10x - 0$$ $$\frac{dy}{dx} = 8x^3 + 10x$$

Comparing this result with the given options:
A. $8x^3 - 20x$
B. $8x^3 + 10x$
C. $x^3 - 10x$
D. $8x^3 - 10x$

The correct option is B.

The final answer is $\boxed{\text{B. } 8x^3 + 10x}$.