question_answer

The value of \[(x+y)(x-y)+\frac{1}{2!}(x+y)(x-y)\]\[({{x}^{2}}+{{y}^{2}})+\frac{1}{3!}(x+y)(x-y)({{x}^{4}}+{{y}^{4}}+{{x}^{2}}{{y}^{2}})+......+\] \[\infty \]is___________.

A)  \[{{e}^{{{x}^{2}}+}}{{e}^{{{y}^{2}}}}\]          

B)  \[{{e}^{{{x}^{2}}-}}^{{{y}^{2}}}\]

C)  \[{{e}^{{{x}^{2}}}}-{{e}^{{{y}^{2}}}}\]

D)  None of these