Add \[ \left(-5 u^{2}+9 u-9\right)+\left(-u^{4}-7 u^{3}+9 u^{2}+2 u+1\right) \]

To add the two polynomial expressions, we first combine like terms. Starting with the first polynomial: \[ -5u^2 + 9u - 9 \] and the second polynomial: \[ -u^4 - 7u^3 + 9u^2 + 2u + 1 \] Now, rearranging them in descending powers of \(u\) gives us: \[ -u^4 - 7u^3 + (-5u^2 + 9u^2) + (9u + 2u) - 9 + 1 \] Combining the like terms: - The \(u^4\) term: \(-u^4\) - The \(u^3\) term: \(-7u^3\) - The \(u^2\) terms: \(-5u^2 + 9u^2 = 4u^2\) - The \(u\) terms: \(9u + 2u = 11u\) - The constant terms: \(-9 + 1 = -8\) Putting it all together, we get: \[ -u^4 - 7u^3 + 4u^2 + 11u - 8 \] So the final answer is: \[ -u^4 - 7u^3 + 4u^2 + 11u - 8 \]