$(4\sin 2x-4\cos x)(2\cos x-1)^2+(4\sin x-4\sin 2x)(2\sin x-1)^2\\ =(4.2\sin x\cos x-4\cos x)(2\cos x-1)^2+(4\sin x-4.2\sin x\cos x)(2\sin x-1)^2\\ =(8\sin x\cos x-4\cos x)(2\cos x-1)^2+(4\sin x-8\sin x\cos x)(2\sin x-1)^2\\ =4\cos x(2\sin x-1)(1-2\cos x)^2+4\sin x(1-2\cos x)(2\sin x-1)^2\\ =4(1-2\cos x)(2\sin x-1)[\cos x(1-2\cos x)+\sin x(2\sin x-1)]\\ =4(1-2\cos x)(2\sin x-1)[\cos x-2\cos^2x+2\sin^2x-\sin x]\\ =4(1-2\cos x)(2\sin x-1)[\cos x-2(\cos^2x-\sin^2x)-\sin x]\\ =4(1-2\cos x)(2\sin x-1)[\cos x-\sin x-2(\cos x-\sin x)(\cos x+\sin x)]\\ =4(1-2\cos x)(2\sin x-1)(\cos x-\sin x)(1-2\cos x-2\sin x)$
