2(sin^6 α +cos^6α)-3(sin^4α+cos^4α)
=2(sin^2α+cos^2α)(sin^4α-sin^2αcos^2α+cos^4α)-3sin^4α-3cos^4α
=-sin^4α-2sin^2αcos^2α-cos^4α
=-(sin^α+cos^2α)^2=-1