trigonometry - How do I prove $cos(4A)= cos^4A-6cos^2Asin^2A+sin^4A$?

I had seen a solution elsewhere to this problem but get stuck on understanding the steps-
please help!

Answer

$\cos(2\cdot 2A)= \cos^2 2A-\sin^2 2A=(\cos^2 A- \sin^2 A)^2-(2\sin A \cos A)^2=\cos^4 A -2\sin^2 A \cos^2 A + \sin^4 A-4 \sin^2 A \cos^2 A$