Question 1199431
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Factoring  x^2 - y^2 = (x+y)*(x-y)  is the standard shortcut, known to all school students of adequate age/grade,

who learn/study Algebra.


So apply this shortcut twice to get

    x^4 - y^4 = (x^2)^2 - (y^2)^2 = (x^2 + y^2)*(x^2 - y^2) = factor (x^2-y^2) again = (x^2 + y^2)*(x+y)*(x-y).
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Solved.