Help with Trigonometric Identities

Sorry for another one but this one is giving me a lot of trouble.

$\displaystyle sin^3{x}cos^2{x}=cos^2{x}sin{x}-cos^4{x}sin{x}$

I assume you would start with the right side since it's the harder side.

I tried changing $\displaystyle cos^2{x}\Rightarrow1-sin^2{x}$ from the RHS, but end up no where. I'm confused at what I should just keep and what I should change with the identity:

$\displaystyle cos^2{x}+sin^2{x}=1$

Edit: Didn't realize there was a sub forum specifically for Trigonometry. Can I move this thread?