What is the difference of the polynomials?

(–2*x*3*y*2 + 4*x*2*y*3 – 3*xy*4) – (6*x*4*y* – 5*x*2*y*3 – *y*5)

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.

Learn how to find the difference of polynomials by subtracting one polynomial from another step-by-step. This problem involves polynomial subtraction and combining like terms. Suitable for Grades 9-12.

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