The given expression is:

\[
2x^4y^5 + 10x^5y^4 - 8x^4y^5
\]

Let's simplify it by combining like terms:

1. Identify the like terms. In this case, \(2x^4y^5\) and \(-8x^4y^5\) are like terms because they have the same powers of \(x\) and \(y\).
   
2. Combine the like terms:
   \[
   (2x^4y^5 - 8x^4y^5) = -6x^4y^5
   \]

3. The expression now becomes:
   \[
   -6x^4y^5 + 10x^5y^4
   \]

Thus, the simplified expression is:

\[
-6x^4y^5 + 10x^5y^4
\]

Would you like further clarification on the simplification process?

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Here are 5 related questions to consider:
1. How do you factor expressions involving multiple variables like \(x\) and \(y\)?
2. Can terms with different exponents on \(x\) and \(y\) ever be combined?
3. How would this expression change if we factored out common terms?
4. What happens if both \(x\) and \(y\) were substituted with numbers?
5. How would the derivative of this expression look?

**Tip:** When simplifying algebraic expressions, always group like terms, which are terms that have the same variables raised to the same powers.

Simplify the polynomial expression 2x⁴y⁵ + 10x⁵y⁴ - 8x⁴y⁵ by combining like terms. This example demonstrates key algebraic concepts, focusing on identifying and simplifying terms with common powers of variables x and y. Suitable for students in Grades 8-10.

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