The expression shown in the image appears to be part of a limit problem, specifically related to the definition of a derivative. Here's the mathematical expression in the image:

$\lim_{\Delta x \to 0} \frac{(x + \Delta x)^2 - 7(x + \Delta x) + 2 - (x^2 - 7x + 2)}{\Delta x}$

This looks like the difference quotient used in finding the derivative of a quadratic function:

$f(x) = x^2 - 7x + 2$

The formula for the derivative using the difference quotient is:

$f'(x) = \lim_{\Delta x \to 0} \frac{f(x + \Delta x) - f(x)}{\Delta x}$

In this case, $f(x) = x^2 - 7x + 2$, so you're calculating:

$f(x + \Delta x) = (x + \Delta x)^2 - 7(x + \Delta x) + 2$

The next step would be expanding and simplifying the numerator, then dividing by $\Delta x$, and finally taking the limit as $\Delta x \to 0$.

Would you like me to go through the full solution step by step?

Here are 5 related questions to explore:

1. What is the purpose of the difference quotient in calculus?
2. How do you expand binomials like $(x + \Delta x)^2$?
3. Why does $\Delta x$ approach 0 in the definition of a derivative?
4. How do you simplify expressions with higher-order terms of $\Delta x$?
5. Can we use this method to find the derivative of any polynomial?

Tip: Always check your algebraic expansions and cancellations carefully when working with limits and derivatives.