Let r = a * b

So, (a * b) * (c * d) = r * (c * d)

=> (a * b) * (c * d) = (r . d)c - (r . c)d                       {since a * (b * c) = (a . c)b - (a . c)c}

=> (a * b) * (c * d) = {(a * b) . d}c - {(a * b) . c}d

=> (a * b) * (c * d) = [a b d]c - [a b c]d                    {since (a * b) . c = [a b c]}