Functions of multiple angles prove the equation

sin B cos^3B - cos B sin^3B = sin 4B/4

How do i prove this equation?
Please EXPLAIN, thanks in advance!

sin4B/4= sinB
please check it. it doesn't sound right.


sinB cos³B -cosB sin³B =

sinB cosB cos²B -cosB sinB sin²B =
factor out sinBcosB

sinBcosB ( cos²B - sin²B) =
use Pythagorian ID

sinBcosB ( 1-sin²B-sin²B) =
sinBcosB (1-2sin²B) =
use double ID

(1/2) sin(2B) (cos(2B) =

use double ID again

(1/2)(1/2)( sin 4B)= (1/4) sin(4B)