Moving out before brackets with XOR

Question

If I had the sum of products like z*a + z*b + z*c + ... + z*y, it would be possible to move the z factor, which is the same, out before brackets: z(a + b + c + ... y).

I'd like to know how it is possible (if it is) to do the same trick if bitwise XOR is used instead of multiplication. z^a + z^b + ... z^y -> z^(a + b + ... + y)

Perhaps a, b, c ... should be preprocessed, such as logically negated or something else, before adding? z could change, so preprocessing, if it's needed, shouldn't depend on particular z value.

Answer 1

From Wikipedia:

Distributivity: with no binary function, not even with itself

So, no, unfortunately, you can't do anything like that with XOR.