sin (x+y) sin (x-y) = sin^2x - sin^2y

i tried doing it but i ended up expanding which turned out ugly..and the result was sin^2x cos^2x - cos^2x sin^2x which did not equal the right side.... the add and subtract formulas are the following:

sin (x+y) = sinx cosy + cosx siny

sin (x-y) = sinx cosy - cosx siny

please answer as soon as possible