The expression in the image is:

$(-4x + 4x^3 + 7) + (-3x^3 - 9 - 3x)$

Now let's simplify the expression step-by-step.

1. Combine like terms:
   • For $x^3$, we have $4x^3 - 3x^3 = 1x^3$.
   • For $x$, we have $-4x - 3x = -7x$.
   • For constants, we have $7 - 9 = -2$.

So, the simplified expression is:

$x^3 - 7x - 2$

Would you like more details or have any questions on this? Here are 5 follow-up questions to expand on this:

1. How do we add polynomials step by step?
2. What happens when we combine like terms with opposite signs?
3. Can we further factor the resulting expression $x^3 - 7x - 2$?
4. What are the different degrees of polynomials and how do we classify them?
5. How do you apply polynomial addition and subtraction in real-world problems?

Tip: Always ensure that you arrange terms of polynomials by their degree before combining like terms to avoid mistakes in simplification.