https://file.aiquickdraw.com/mathbot/file/1729227644411d8cbp0xs.jpg

The given expression to simplify is:

\[
(8x + 3z - 8z^2) + (4y - 5z)
\]

To group like terms together, let's rearrange and combine terms based on their variables:

1. Group terms with \(x\), \(y\), \(z\), and \(z^2\):
   \[
   8x + 4y + 3z + (-5z) - 8z^2
   \]

2. Combine the like terms for \(z\):
   \[
   3z + (-5z) = -2z
   \]

So, the final expression with like terms grouped together is:

\[
8x + 4y - 2z - 8z^2
\]

Looking at the answer choices, the correct one is:

\[
\boxed{8x + 4y + [-8z^2] + [3z + (-5z)]}
\]

This corresponds to the fourth option in the image.

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Would you like further details or have any questions? Here are five related questions to consider:

1. What are like terms, and why do we group them?
2. How do you handle variables raised to different powers when combining terms?
3. What steps should you follow to simplify polynomial expressions?
4. Can you factor the resulting expression for further simplification?
5. How can you check your final answer to ensure correctness?

**Tip:** Always ensure to match the correct sign when combining like terms, especially if negative values are involved.

Which expression shows the sum of the polynomials with like terms grouped together? The polynomials are (8x + 3z - 8z^2) + (4y - 5z).

Learn how to simplify the sum of two polynomials by grouping like terms. This problem involves adding (8x + 3z - 8z^2) and (4y - 5z) and then simplifying. It's suitable for students in Grades 7-9.

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