Factor the expression completely over the complex numbers. x^4 − 625 enter your answer in the box.

You have to observe that and 625 are both squares (of and 25, respectively). So, you can use the "difference of square" pattern for factorization:

to write

Note that, again, is a difference of square:

On the other hands, admits no factorization, because it's a second-degree polynomial (thus a parabola) with no solutions.

So, the whole expression becomes

(x-5)(x+5)(x-5i)(x+5i)

Step-by-step explanation:

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1) 2/5

2) zero=0/1

3) zero=0/2

4) -4/5

5) undefined=3/0