Is correct the factorización so far?

Question

I have this exercise, that i must factor it.

$4 - 64a^2b^2c^4d^8$

I resolve like this:

$= (2 - 8abc^2d^4)(2 + 8abc^2d^4)$

According to the exercise guide, this is the final result.

But, should not it be further factorized? , because it can be divided even between 2.

$2(1 - 4abc^2d^4)2(1 + 4abc^2d^4)$

Is my thought correct? Is it necessary? or is it totally wrong?

Answer 1

Yes, you can further factorize them that way.

$$2^2(1 - 4abc^2d^4)(1 + 4abc^2d^4)$$

Answer 2

the searched result should be $$-4 \left(4 a b c^2 d^4-1\right) \left(4 a b c^2 d^4+1\right)$$