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The given expression is:

\[
5x^8y - 2xy^3 + x^3
\]

To collect like terms, we need to identify terms that have the same combination of variables raised to the same powers. In this case:

- \(5x^8y\)
- \(-2xy^3\)
- \(x^3\)

None of these terms share the same combination of variables and exponents, so they cannot be combined. Therefore, the simplified expression remains:

\[
5x^8y - 2xy^3 + x^3
\]

Would you like further clarification on this, or have any questions?

Here are some follow-up questions you might find useful:
1. What are like terms in algebraic expressions?
2. How do we simplify polynomials with more variables?
3. Can like terms have different variables?
4. What is the process for factoring algebraic expressions?
5. How do exponents affect the collection of like terms?

**Tip:** When collecting like terms, always check that both the variables and their exponents match exactly!

Learn how to collect like terms in polynomials such as 5x^8y - 2xy^3 + x^3. This problem demonstrates the rules for identifying and combining terms with the same variables and exponents. Suitable for students in Grades 8-10.

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