You are given the function $f(x+h) = 2(x+h)^2 + 3(x+h) - 1$. To simplify this expression, we'll expand and combine like terms.

Step 1: Expand the squared term

$(x+h)^2 = x^2 + 2xh + h^2$

Step 2: Substitute into the function

$f(x+h) = 2(x^2 + 2xh + h^2) + 3(x+h) - 1$

Step 3: Distribute the constants

$f(x+h) = 2x^2 + 4xh + 2h^2 + 3x + 3h - 1$

Step 4: Combine like terms

$f(x+h) = 2x^2 + 4xh + 2h^2 + 3x + 3h - 1$

So, the expanded form of $f(x+h)$ is: $f(x+h) = 2x^2 + 4xh + 2h^2 + 3x + 3h - 1$

Would you like further details or have any questions on this? Here are five questions to expand the topic:

1. How does the function $f(x) = 2x^2 + 3x - 1$ look when you substitute specific values of $h$?
2. What happens when you calculate the derivative of $f(x)$?
3. How do you find the limit of $f(x+h)$ as $h$ approaches 0?
4. What is the significance of the terms $4xh$ and $2h^2$ in this context?
5. How would this process change if the original function