$\begin{array}{l}a) \quad 2\sin^2x-\sin x - 1 =0\\ \Leftrightarrow (\sin x - 1)(2\sin x + 1) =0\\ \Leftrightarrow \left[\begin{array}{l}\sin x = 1\\\sin x =-\dfrac12\end{array}\right.\\ \Leftrightarrow \left[\begin{array}{l}x = \dfrac{\pi}{2} + k2\pi\\x = -\dfrac{\pi}{6} + k2\pi\\x = \dfrac{7\pi}{6} + k2\pi\end{array}\right.\quad (k\in\Bbb Z)\\ b)\quad (x - 2y)^6\\ =C_6^0x^6.(-2y)^0 + C_6^1x^5.(-2y)^1 + C_6^2x^4.(-2y)^2 + \\ +C_6^3x^3.(-2y)^3 + C_6^4x^2.(-2y)^4 + C_6^5x^1(-2y)^5 + C_6^6x^0.(-2y)^6\\ = x^6 - 12x^5y +60x^4y^2 - 160x^3y^3 + 240x^2y^4 - 192xy^5 +64y^6 \end{array}$
