You have to observe that [tex] x^4 [/tex] and 625 are both squares (of [tex] x^2 [/tex] and 25, respectively). So, you can use the "difference of square" pattern for factorization:
[tex] a^2-b^2 = (a+b)(a-b) [/tex]
to write
[tex] x^4 - 625 = (x^2+25)(x^2-25) [/tex]
Note that, again, [tex]x^2-25[/tex] is a difference of square:
[tex] x^2-25 = (x+5)(x-5) [/tex]
On the other hands, [tex] x^2+25 [/tex] admits no factorization, because it's a second-degree polynomial (thus a parabola) with no solutions.
So, the whole expression becomes
[tex] x^4 - 625 = (x^2+25)(x+5)(x-5) [/tex]
Answer:
(x-5)(x+5)(x-5i)(x+5i)
Step-by-step explanation:
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