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The given expression is:

\[
xy - 2xy + 3x^2y - 4xy^2 + 2xy^2
\]

### Step 1: Combine Like Terms
We can group the terms that are similar:

\[
xy - 2xy = -xy
\]
\[
-4xy^2 + 2xy^2 = -2xy^2
\]

Thus, the simplified polynomial becomes:

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

### Step 2: Substitute \(x = 4\) and \(y = -2\)
Now we substitute the values \(x = 4\) and \(y = -2\) into the simplified expression:

\[
-xy = -(4)(-2) = 8
\]
\[
3x^2y = 3(4^2)(-2) = 3(16)(-2) = -96
\]
\[
-2xy^2 = -2(4)(-2^2) = -2(4)(4) = -32
\]

### Step 3: Add the Results
Now, sum up the terms:

\[
8 + (-96) + (-32) = 8 - 96 - 32 = -120
\]

So the correct answer is:
\[
\boxed{-xy - 2xy^2 + 3x^2y; -120}
\]

The correct option matches the second choice.

Would you like more details or have any further questions?

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Here are 5 related questions for practice:
1. How do you identify like terms in a polynomial?
2. What happens when you substitute negative values into polynomial expressions?
3. How do exponents affect the calculation when substituting values into a polynomial?
4. How can you quickly simplify polynomials with multiple like terms?
5. How does factoring polynomials relate to combining like terms?

**Tip:** Always simplify expressions before substituting values to avoid unnecessary complications.

Combine like terms in the given polynomial. Then, evaluate for x = 4, y = -2. xy - 2xy + 3x²y - 4xy² + 2xy²

Learn how to combine like terms in the polynomial expression xy - 2xy + 3x²y - 4xy² + 2xy² and evaluate it for x = 4 and y = -2. This step-by-step guide covers simplifying polynomials and substituting values.

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