An Extrapolation of a Beautiful Series

Calculus Level 3

(x+y)(xy)+12!(x+y)(xy)(x2+y2)+13!(x+y)(xy)(x4+y4+x2y2)+= ? \begin{aligned} && (x+y)(x-y) \\ &&+ \dfrac{1}{2!} (x+y)(x-y)(x^2 + y^2) \\ &&+ \dfrac{1}{3!} (x+y)(x-y)(x^4 + y^4 + x^2 y^2 ) \\ &&+ \ldots \\ &&= \ ? \end{aligned}

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