Factor Completely: X^4-2x^2-8

Treat your expression as a quadratic one. You can replace x^2 by y for example.

Let x^2 = y

Then,

y^2 - 2y - 8 = (y-4)(y+2)

Then, replace your x.

(y-4)(y+2)= (x^2 -4)(x^2+2)

It's nearly done. Can you complete it?

Hint, remember that:

(a^2 - b^2) = (a+b)(a-b)