To find the difference of the polynomials, we'll subtract the second polynomial from the first.

Given polynomials:

$(-2x^3y^2 + 4x^2y^3 - 3xy^4) - (6x^4y - 5x^2y^3 - y^5)$

Step 1: Distribute the negative sign

First, distribute the negative sign to each term in the second polynomial:

$-2x^3y^2 + 4x^2y^3 - 3xy^4 - 6x^4y + 5x^2y^3 + y^5$

Step 2: Combine like terms

Now, combine the like terms:

• The term $x^4y$ only appears as $-6x^4y$.
• The terms involving $x^3y^2$ and $xy^4$ do not have counterparts to combine with, so they remain $-2x^3y^2$ and $-3xy^4$.
• The terms involving $x^2y^3$ combine as $4x^2y^3 + 5x^2y^3 = 9x^2y^3$.
• The term involving $y^5$ is $y^5$.

So, the result is:

$-6x^4y - 2x^3y^2 + 9x^2y^3 - 3xy^4 + y^5$

Final Answer:

The difference of the polynomials is:

$\boxed{-6x^4y - 2x^3y^2 + 9x^2y^3 - 3xy^4 + y^5}$

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Do you want more details or have any questions?

Here are 5 related questions to consider:

1. What is the sum of the polynomials instead of the difference?
2. How would the result change if the exponents of $x$ and $y$ were interchanged in the original polynomials?
3. What happens if we factor the resulting polynomial?
4. Can you evaluate the resulting polynomial for specific values of $x$ and $y$?
5. How does the polynomial change if the coefficients are squared?

Tip: When subtracting polynomials, ensure you distribute the negative sign correctly across all terms of the second polynomial.