Chứng minh: ${\sin ^4}x + {\cos ^4}x = 1 - 2{\sin ^2}x{\cos ^2}x$.

$VT = {\left( {{{\sin }^4}x + 2{{\sin }^2}x.{{\cos }^2}x + {{\cos }^4}x} \right)^2} - 2{\sin ^2}x.{\cos ^2}x$

$= {\left( {{{\sin }^2}x + {{\cos }^2}x} \right)^2} - 2{\sin ^2}x.{\cos ^2}x = 1 - 2{\sin ^2}x.{\cos ^2}x = VP$ ⇒ đpcm