Which expression shows the sum of the polynomials with like terms grouped together?

1. Identify the polynomials: The problem asks to find the sum of two polynomials: $(8x + 3z - 8z^2)$ and $(4y - 5z)$.
2. Write the sum: The sum can be written as $(8x + 3z - 8z^2) + (4y - 5z)$.
3. Remove parentheses: Since we are adding the polynomials, we can remove the parentheses without changing the signs of the terms: $8x + 3z - 8z^2 + 4y - 5z$.
4. Group like terms: Identify terms with the same variables raised to the same powers. In this expression, the like terms are $3z$ and $-5z$.
5. Rearrange and group: Rearrange the terms to group the like terms together. We can also group terms that do not have like terms with others to prepare for the final answer format. A common way to present this is to group terms with the same variable together, and to use brackets for clarity when grouping.
- The term $8x$ has no other like terms.
- The term $4y$ has no other like terms.
- The term $-8z^2$ has no other like terms.
- The terms $3z$ and $-5z$ are like terms.
We can group these as $8x + 4y + (-8z^2) + [3z + (-5z)]$. This expression shows the sum with like terms grouped together in the brackets.