a,
$A=3(\sin^4\alpha+\cos^4\alpha)-2(\sin^6\alpha+\cos^6\alpha)$
$=-2(\sin^2\alpha+\cos^2\alpha)(\sin^4\alpha-\sin^2\alpha\cos^2\alpha+\cos^4\alpha)+3(\sin^4\alpha+\cos^4\alpha)$
$=-2\sin^4\alpha+2\sin^2\alpha\cos^2\alpha-2\cos^4\alpha+3\sin^4\alpha+3\cos^4\alpha$
$=(\sin^2\alpha)^2+2\sin^2\alpha\cos^2\alpha+(\cos^2\alpha)^2$
$=(\sin^2\alpha+\cos^2\alpha)^2$
$=1^2$
$=1$
b,
$B=\sin^6a+\cos^6\alpha+3\sin^2\alpha\cos^2\alpha$
$=(\sin^2\alpha+\cos^2\alpha)(\sin^4\alpha-\sin^2\alpha\cos^2\alpha+\cos^4\alpha)+3\sin^2\alpha\cos^2\alpha$
$=(\sin^2\alpha)^2+2\sin^2\alpha\cos^2\alpha+(\cos^2\alpha)^2$
$=(\sin^2\alpha+\cos^2\alpha)^2$
$=1^2$
$=1$