To find $f(a+h) - f(a)$ for the function $f(x) = x^3 + 2x - 1$, let's follow these steps:

1. Substitute $a + h$ into the function $f(x)$: $f(a+h) = (a+h)^3 + 2(a+h) - 1$

2. Expand $(a+h)^3$: $(a+h)^3 = a^3 + 3a^2h + 3ah^2 + h^3$ So, $f(a+h) = a^3 + 3a^2h + 3ah^2 + h^3 + 2a + 2h - 1$

3. Calculate $f(a)$: $f(a) = a^3 + 2a - 1$

4. Subtract $f(a)$ from $f(a+h)$: $f(a+h) - f(a) = \left( a^3 + 3a^2h + 3ah^2 + h^3 + 2a + 2h - 1 \right) - \left( a^3 + 2a - 1 \right)$

5. Simplify by canceling terms: $f(a+h) - f(a) = 3a^2h + 3ah^2 + h^3 + 2h$

Thus, the result is: [ f(a