how do you factor 2x^4 - 2y^4

First factor out 2

2 (x^4 - y^4)

Rewrite it as ((x^2) ^2) and ((y^2) ^2)

Then you get ...

2 ((x^2) ^2) - (y^2) ^2))

Now both terms are perfect squares, factor using the difference of squares formula, a^2 + b^2 = (a+b) (a-b)

a = x^2 and b = y^2

2 ((x^2 + y^2) (x+y) (x-y))

clean it up!

2 (x^2 + y^2) (x+y) (x-y)