Use operations to simplify the following polynomials. \( \begin{array}{ll}\text { 1. }(3 x+4)+(2 x-5) & \text { 2. }\left(5 x^{3}+2 x^{2}-1\right)+\left(2 x-8 x^{3}+10\right) \\ \text { 3. }\left(2 x^{3}+5 x^{2}-3 x+7\right)+\left(5 x^{3}+x^{2}+9\right) & \text { 4. }\left(6 x^{3}+7 x-5\right)-\left(x^{3}-10 x+5\right) \\ \text { 5. }(12 x-6)-(4 x-8) & \text { 6. }\left(3 x^{3}-2 x^{2}+7 x+5\right)-\left(5 x^{2}+11 x+3\right)\end{array} \)

1. \[ (3x + 4) + (2x - 5) = 3x + 2x + 4 - 5 = 5x - 1. \] 2. \[ (5x^3 + 2x^2 - 1) + (2x - 8x^3 + 10) = \underbrace{5x^3 - 8x^3}_{-3x^3} + 2x^2 + 2x + \underbrace{(-1 + 10)}_{9} = -3x^3 + 2x^2 + 2x + 9. \] 3. \[ (2x^3 + 5x^2 - 3x + 7) + (5x^3 + x^2 + 9) = \underbrace{2x^3 + 5x^3}_{7x^3} + \underbrace{5x^2 + x^2}_{6x^2} - 3x + \underbrace{7 + 9}_{16} = 7x^3 + 6x^2 - 3x + 16. \] 4. \[ (6x^3 + 7x - 5) - (x^3 - 10x + 5) = 6x^3 + 7x - 5 - x^3 + 10x - 5 = \underbrace{6x^3 - x^3}_{5x^3} + \underbrace{7x + 10x}_{17x} - \underbrace{5 + 5}_{10} = 5x^3 + 17x - 10. \] 5. \[ (12x - 6) - (4x - 8) = 12x - 6 - 4x + 8 = \underbrace{12x - 4x}_{8x} + \underbrace{-6 + 8}_{2} = 8x + 2. \] 6. \[ (3x^3 - 2x^2 + 7x + 5) - (5x^2 + 11x + 3) = 3x^3 - 2x^2 + 7x + 5 - 5x^2 - 11x - 3 = 3x^3 - \underbrace{2x^2 + 5x^2}_{7x^2} + \underbrace{7x - 11x}_{-4x} + (5 - 3) = 3x^3 - 7x^2 - 4x + 2. \]