Add the polynomials. (Simplify your answer completely.) \[ \left(-7 a^{2}-a b+17 b^{2}\right)+\left(8 a^{2}-b^{2}\right) \] SUBMIT ANSWER

Let's start by combining the polynomials: \[ \left(-7 a^{2} - a b + 17 b^{2}\right) + \left(8 a^{2} - b^{2}\right) \] Now, we can group like terms: - For \(a^{2}\): \(-7 a^{2} + 8 a^{2} = 1 a^{2}\) - For \(b^{2}\): \(17 b^{2} - 1 b^{2} = 16 b^{2}\) - For \(ab\): \(-a b\) (no other \(ab\) terms to combine) Putting it all together, we get: \[ 1 a^{2} - a b + 16 b^{2} \] So, the simplified answer is: \[ a^{2} - a b + 16 b^{2} \]