To add the given polynomial expressions (-5a^3 - 2a^2) and (6a^3 + 9a^2 + 8a), you simply combine like terms:
(-5a^3 - 2a^2) + (6a^3 + 9a^2 + 8a) = (6a^3 - 5a^3) + (9a^2 - 2a^2) + 8a
Now, perform the operations within the parentheses:
1. 6a^3 - 5a^3 = a^3
2. 9a^2 - 2a^2 = 7a^2
So, the simplified expression is:
a^3 + 7a^2 + 8a