$A= $2\sin^4x-\sin^4x+\sin^2x.\cos^2x+3\sin^2x$
$= \sin^4x+\sin^2x\cos^2x+\sin^2x+2\sin^2x$
$= \sin^4x+\sin^2x(\cos^2x+1)+2\sin^2x$
$= \sin^4x+\sin^2x(2\cos^2x+\sin^2x)+2\sin^2x$
$= 2\sin^4x+2\sin^2x\cos^2x+2\sin^2x$
$= 2\sin^2x(\sin^2x+\cos^2x)+2\sin^2x$
$= 2\sin^2x+2\sin^2x$
$= 4\sin^2x$ (Không CM được).