$2sin^6\alpha + 2cos^2\alpha + 6sin^2\alpha.cos^2\alpha$
$=2sin^2\alpha (sin^4\alpha - 1) + 2 + \frac{3}{2}sin^22\alpha$
$=2sin^2\alpha(sin^2\alpha +1)(sin^2\alpha-1) +2+ \frac{3}{2}sin^22\alpha$
$=2sin^2\alpha(sin^2\alpha +1)(-cos^2\alpha) +2+ \frac{3}{2}sin^22\alpha$
$=\frac{-1}{2}sin^22\alpha(sin^2\alpha+1) +2+ \frac{3}{2}sin^22\alpha$
$=\frac{-1}{2}sin^22\alpha(sin^2\alpha + 1 -3) +2$
$=\frac{-1}{2}sin^22\alpha(sin^2\alpha -2) +2$