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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!

Which of the following expressions is equivalent to: (4x^3 - 5x) + (8x - 3x^3)?

Learn how to simplify the polynomial expression (4x^3 - 5x) + (8x - 3x^3) by combining like terms. This solution is suitable for students in Grades 8-10 and covers important algebraic concepts such as polynomials and like terms.

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