Verifying Trig identity

Question

Hello! I am having some trouble verifying a trig identity

 

sin(4x)=4cos^3(x)sin(x)-4sin^3(x)cos(x)

Answer 1

sin 2x = 2sin x cos x

sin (4x) = sin (2x+2x) = 2 sin 2x cos 2x = 2 (2 sin x cos x)(cos²x - sin²x)

 

Finish, please.