(7n-n-8n^{4}) + (5n+4n^{3}+5n^{4})
(7n-n-8n^{4})+(5n+4n^{3}+5n^{4})
Since all of the operations are addition and subtraction, we can remove the parentheses:
7n - n - 8n^{4} + 5n + 4n^{3} + 5n^{4}
Now combine like-terms. Like terms have the same variable and exponent. I'll group the like terms in parentheses so you can see them:
(-8n^{4} + 5n^{4}) + (4n^{3}) + (7n - n +5n)
-3n^{4} + 4n^{3} + 11n