grouping like terms in polynomial addition

1. Identify the terms in the expression: The given expression is $(3a^2 - 5ab + b^2) + (-3a^2 + 2b^2 + 8ab)$. We need to identify all the individual terms: $3a^2$, $-5ab$, $b^2$, $-3a^2$, $2b^2$, and $8ab$.

2. Group like terms: Like terms are terms that have the same variables raised to the same powers.
- Terms with $a^2$: $3a^2$ and $-3a^2$. Grouping these gives $[3a^2 + (-3a^2)]$.
- Terms with $ab$: $-5ab$ and $8ab$. Grouping these gives $(-5ab + 8ab)$.
- Terms with $b^2$: $b^2$ and $2b^2$. Grouping these gives $(b^2 + 2b^2)$.

1. Combine the groups: Putting these groups together, we get the expression: $[3a^2 + (-3a^2)] + (-5ab + 8ab) + (b^2 + 2b^2)$.

1. Compare with the options: Looking at the provided choices, the second option matches our derived expression: $[3a^2 + (-3a^2)] + (-5ab + 8ab) + (b^2 + 2b^2)$.