Question

Factor the following completely
x^4 – 625

Answer 1

call y = x^2 so x = +/- sqrt y
then
y^2 = 625
y = 25 or y = -25
x = sqrt 25 = +5 or -5
y = sqrt-25 = +5i or -5i

Answer 2

Any expression of the form a^2 - b^2 can be written as (a + b)(a - b).

Therefore, x^4 - 625) = (x^2 + 25)(x^2 - 25).

Then, (x^2 + 25)(x + 5)(x - 5)