A.
$\ln 2+\frac{x+y}{2}-\frac{1}{8}({{x}^{2}}-2xy+{{y}^{2}})+o({{x}^{2}}+{{y}^{2}})$
B.
$\ln 2+\frac{x+y}{2}-\frac{1}{4}({{x}^{2}}-2xy+{{y}^{2}})+o({{x}^{2}}+{{y}^{2}})$
C.
$\ln 2+\frac{x+y}{2}+\frac{1}{4}({{x}^{2}}-2xy+{{y}^{2}})+o({{x}^{2}}+{{y}^{2}})$
D.
$\ln 2+\frac{x+y}{2}+\frac{1}{8}({{x}^{2}}-2xy+{{y}^{2}})+o({{x}^{2}}+{{y}^{2}})$