$\frac12\{(a+b)^2-(a-b)^2\}$
$=\frac12\{(a^2+2ab+b^2)-(a^2-2ab+b^2)\}$
$=\frac12\left(a^2+2ab+b^2-a^2+2ab-b^2\right)$
$=\frac12\cdot4ab$
$=2ab$