Giải thích các bước giải:
$\begin{array}{l}
2\left( {{{\sin }^6}\alpha + {{\cos }^6}\alpha} \right) + 1\\
= 2\left( {{{\left( {{{\sin }^2}\alpha} \right)}^3} + {{\left( {{{\cos }^2}\alpha} \right)}^3}} \right) + 1\\
= 2\left( {{{\sin }^2}\alpha + {{\cos }^2}\alpha} \right)\left( {{{\left( {{{\sin }^2}\alpha} \right)}^2} - {{\sin }^2}\alpha{{\cos }^2}\alpha + {{\left( {{{\cos }^2}\alpha} \right)}^2}} \right) + 1\\
= 2\left( {{{\left( {{{\sin }^2}\alpha} \right)}^2} - {{\sin }^2}\alpha{{\cos }^2}\alpha + {{\left( {{{\cos }^2}\alpha} \right)}^2}} \right) + 1\left( {do:{{\sin }^2}\alpha + {{\cos }^2}\alpha = 1} \right)\\
= 2\left( {{{\sin }^4}\alpha + {{\cos }^4}\alpha} \right) + 1 - 2{\sin ^2}\alpha{\cos ^2}\alpha\\
= 2\left( {{{\sin }^4}\alpha + {{\cos }^4}\alpha} \right) + {\left( {{{\sin }^2}\alpha + {{\cos }^2}\alpha} \right)^2} - 2{\sin ^2}\alpha{\cos ^2}\alpha\\
= 2\left( {{{\sin }^4}\alpha + {{\cos }^4}\alpha} \right) + {\sin ^4}\alpha + {\cos ^4}\alpha + 2{\sin ^2}\alpha{\cos ^2}\alpha - 2{\sin ^2}\alpha{\cos ^2}\alpha\\
= 3\left( {{{\sin }^4}\alpha + {{\cos }^4}\alpha} \right)
\end{array}$
