Rewrite as .

Let . Substitute for all occurrences of .

Rewrite as .

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

Rewrite the polynomial.

Factor using the perfect square trinomial rule , where and .

Replace all occurrences of with .

Rewrite as .

Since both terms are perfect squares, factor using the difference of squares formula, where and .

Apply the product rule to .

Factor x^4-2x^2+1