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The given expression is:

\[
10x^2y + 2xy^2 - 4x^2 - 4x^2y
\]

To find the sum of the polynomials with like terms grouped together, let's group and simplify the expression step by step:

1. Combine the like terms:
   - Terms with \(x^2y\): \(10x^2y - 4x^2y = 6x^2y\)
   - The term \(2xy^2\) has no like terms, so it remains as it is.
   - The term \(-4x^2\) also remains unchanged.

Now, the simplified expression is:

\[
6x^2y + 2xy^2 - 4x^2
\]

Looking at the options, the correct choice would be the one grouping like terms together as follows:

\[
\boxed{[10x^2y + 2xy^2] + (-4x^2y) + (-4x^2)}
\]

The fourth option matches this format, where the terms are grouped based on their similarity.

Would you like more details or have any questions?

Here are some related questions you might consider:
1. What are like terms in polynomials?
2. How do you combine like terms in an expression?
3. What is the importance of grouping terms when simplifying?
4. How do exponents affect the classification of like terms?
5. How can you distribute negative signs across grouped terms?

**Tip**: Always double-check for similar variables and exponents when grouping like terms to avoid mistakes in simplification.

Which expression shows the sum of the polynomials with like terms grouped together? 10x^2y + 2xy^2 - 4x^2 - 4x^2y

Learn how to sum polynomials by grouping like terms in the expression 10x^2y + 2xy^2 - 4x^2 - 4x^2y. This solution covers core algebra concepts, including identifying and combining like terms. Suitable for students in Grades 7-9.

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