Complete the statement. (3a^2 - 5ab + b^2) - (-3a^2 + 2b^2 + 8ab) =

1. Distribute the negative sign: The expression involves subtracting the second polynomial from the first. This means we need to distribute the negative sign to each term in the second polynomial. So, $-( -3a^2 + 2b^2 + 8ab )$ becomes $+3a^2 - 2b^2 - 8ab$. The expression is now $3a^2 - 5ab + b^2 + 3a^2 - 2b^2 - 8ab$.
2. Group like terms: Identify terms with the same variables raised to the same powers. In this expression, the like terms are $3a^2$ and $3a^2$, $-5ab$ and $-8ab$, and $b^2$ and $-2b^2$.
3. Combine like terms: Add or subtract the coefficients of the like terms.
- For the $a^2$ terms: $3a^2 + 3a^2 = 6a^2$.
- For the $ab$ terms: $-5ab - 8ab = -13ab$.
- For the $b^2$ terms: $b^2 - 2b^2 = -b^2$.
4. Write the simplified expression: Combine the results from the previous step to form the final simplified polynomial.