Ejercicio 3. Reduce las siguientes expresiones, realizando las operaciones correspondientes. \begin{tabular}{ll|l}\hline 1) \( x+2 y+5 x^{2} y-9 x+7 x-3 y-3 y-12 x^{2} y= \) & 4) \( 3 \sqrt{2}-5 \sqrt{3}+\sqrt{2}-11 \sqrt{3}+5 \sqrt{2}+20 \sqrt{3}= \) \\ 2) \( \frac{1}{2} x y-\frac{3}{4} a b+\frac{5}{2} x y+\frac{2}{3} a b-\frac{1}{6} a b+\frac{7}{2} x y= \) & 5) \( \operatorname{sen} x+2 \cos ^{2} x+5 \operatorname{sen} x-3 \cos ^{2} x-8 \operatorname{sen} x \) \\ 3) \( 2 x^{2} y z-3 x y^{2} z+5 x y z^{2}-7 x y^{2} z-x^{2} y z+6 x y z^{2}= \) & \end{tabular}

1) \( x + 2y + 5x^{2}y - 9x + 7x - 3y - 3y - 12x^{2}y = -x + 2x^{2}y \) 2) \( \frac{1}{2}xy - \frac{3}{4}ab + \frac{5}{2}xy + \frac{2}{3}ab - \frac{1}{6}ab + \frac{7}{2}xy = 8xy + \left( \frac{2}{3} - \frac{3}{4} - \frac{1}{6} \right) ab = 8xy - \frac{1}{12} ab \) 3) \( 2x^{2}yz - 3xy^{2}z + 5xyz^{2} - 7xy^{2}z - x^{2}yz + 6xyz^{2} = (2x^{2}yz - x^{2}yz) + (-3xy^{2}z - 7xy^{2}z) + (5xyz^{2} + 6xyz^{2}) = x^{2}yz - 10xy^{2}z + 11xyz^{2} \) 4) \( 3\sqrt{2} - 5\sqrt{3} + \sqrt{2} - 11\sqrt{3} + 5\sqrt{2} + 20\sqrt{3} = (3\sqrt{2} + \sqrt{2} + 5\sqrt{2}) + (-5\sqrt{3} - 11\sqrt{3} + 20\sqrt{3}) = 9\sqrt{2} + 4\sqrt{3} \) 5) \( \sin x + 2\cos^{2}x + 5\sin x - 3\cos^{2}x - 8\sin x = (1 + 5 - 8)(\sin x) + (2 - 3)(\cos^{2}x) = -2\sin x - \cos^{2}x \)