We are given the following expression to simplify:

$(4x^3 - 5x) + (8x - 3x^3)$

Let's break it down step by step:

1. Group the like terms (terms with the same power of $x$):

   • $4x^3 - 3x^3$ (terms with $x^3$)
   • $-5x + 8x$ (terms with $x$)

2. Simplify each group:

   • $4x^3 - 3x^3 = x^3$
   • $-5x + 8x = 3x$

3. Combine the results: $x^3 + 3x$

Thus, the expression simplifies to:

$x^3 + 3x$

The correct answer is A) $x^3 + 3x$.

Would you like more details, or do you have any questions?

Here are 5 related questions to further explore this topic:

1. How do you identify like terms in a polynomial expression?
2. What are some strategies for simplifying polynomials with multiple variables?
3. How do you factor a polynomial after simplifying it?
4. What is the degree of the expression $x^3 + 3x$?
5. How would the process differ if there were fractional exponents?

Tip: Always start by grouping like terms when simplifying expressions—this makes the process much easier!