13. [-/1 Points] DETAILS MY NOTES TGEIALG6 5.5.066. Perform the operations. (Simplify your answer completely.) Subtract \( \left(36 x^{2}-18 x+51\right) \) from the sum of \( \left(24 x^{2}-12 x-9\right) \) and \( \left(-17 x^{2}+12 x+9\right) \). \( \square \) SUBMIT ANSWER

First, let's find the sum of the two polynomials: \((24 x^{2} - 12 x - 9) + (-17 x^{2} + 12 x + 9)\) Combine like terms: \( (24x^{2} - 17x^{2}) + (-12x + 12x) + (-9 + 9) = 7x^{2} + 0x + 0 = 7x^{2}\). Now, we need to subtract the first polynomial from this result: \(7x^{2} - (36x^{2} - 18x + 51)\). Distributing the negative sign gives us: \(7x^{2} - 36x^{2} + 18x - 51\). Combine like terms: \((7x^{2} - 36x^{2}) + (18x) + (-51) = -29x^{2} + 18x - 51\). So the final answer after simplification is: \(-29x^{2} + 18x - 51\).