Question

PLEASE HELP ASAP!!! CORRECT ANSWERS ONLY PLEASE!!! I CANNOT RETAKE THIS!!

Factor the expression completely over the complex numbers.

x^4 − 625

Answer 1

$\text{Use}\\\\a^2-b^2=(a-b)(a+b)\\\\i=\sqrt{-1}\to i^2=-1\\---------------------\\\\x^4-625=(x^2)^2-25^2=(x^2-25)(x^2+25)\\\\=(x^2-5^2)(x^2+5^2)=(x-5)(x+5)[x^2-(-1)(5^2)]\\\\=(x-5)(x+5)[x^2-(i^2)(5^2)]=(x-5)(x+5)[x^2-(5i)^2]\\\\=(x-5)(x+5)(x-5i)(x+5i)$