56)

$\begin{array}{l} A = 4\left[ {{{\sin }^4}x + {{\cos }^4}\left( {x + \dfrac{\pi }{4}} \right)} \right] - 3;x = \dfrac{\pi }{8}\\ A = 4\left[ {{{\sin }^4}\dfrac{\pi }{8} + {{\cos }^4}\left( {\dfrac{\pi }{8} + \dfrac{\pi }{4}} \right)} \right] - 3\\ A = 4\left[ {{{\sin }^4}\dfrac{\pi }{8} + {{\cos }^4}\left( {\dfrac{\pi }{2} - \dfrac{\pi }{8}} \right)} \right] - 3\\ A = 4\left[ {{{\sin }^4}\dfrac{\pi }{8} + {{\sin }^4}\dfrac{\pi }{8}} \right] - 3\\ A = 8{\sin ^4}\dfrac{\pi }{8} - 3 = 8.{\left( {\dfrac{{1 - \cos \dfrac{\pi }{4}}}{2}} \right)^2} - 3 = 8.\dfrac{{{{\left( {1 - \cos \dfrac{\pi }{4}} \right)}^2}}}{4} - 3\\ A = 2{\left( {1 - \cos \dfrac{\pi }{4}} \right)^2} - 3 = 2{\left( {1 - \dfrac{{\sqrt 2 }}{2}} \right)^2} - 3 =  - 2\sqrt 2  \to B \end{array}$  

57/

$\begin{array}{l} 2\left( {{{\sin }^6}x + {{\cos }^6}x} \right) - 3\left( {{{\sin }^4}x + {{\cos }^4}x} \right)\\  = 2\left( {{{\sin }^2}x + {{\cos }^2}x} \right)\left( {{{\sin }^4}x - {{\sin }^2}x.{{\cos }^2}x + {{\cos }^4}x} \right) - 3\left[ {{{\left( {{{\sin }^2}x + {{\cos }^2}x} \right)}^2} - 2{{\sin }^2}x{{\cos }^2}x} \right]\\  = 2\left[ {{{\left( {{{\sin }^2}x + {{\cos }^2}x} \right)}^2} - 3{{\sin }^2}x.{{\cos }^2}x} \right] - 3\left( {1 - 2{{\sin }^2}x{{\cos }^2}x} \right)\\  = 2\left( {1 - 3{{\sin }^2}x{{\cos }^2}x} \right) - 3\left( {1 - 2{{\sin }^2}x{{\cos }^2}x} \right)\\  =  - 1 \end{array}$