\(\displaystyle 4(f,g) = \Vert f+g\Vert ^2 - \Vert f-g\Vert ^2

= \int \vert f+g\vert ^2dx -\int \vert f-g \vert ^2dx \)

\(\displaystyle = \int (f+g)(\bar{f} +\bar{g})-(f-g)(\bar{f} -\bar{g})dx

= 2\int \bar{f} g +f\bar{g}dx\)

But I want to end up with \(\displaystyle 4\int f\bar{g} dx\). I assume I've gone wrong somewhere???