Originally Posted by

**markwolfson16900** I'm trying to derive the $\displaystyle L^2(\mathbb{R} )$ inner product using the polarization identity but I'm getting stuck. This is how far I get

$\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???