Factorization of x^4 + 4

x^4 + 4
= x^4 + 4x^2 + 4 - 4x^2, adding and subtracting 4x^2 (the value remains unchanged)
= (x^4 + 4x^2 + 4) - 4x^2
= (x^2 + 2)^2 - 4x^2, since (A + B)^2 = A^2 + B^2
= (x^2 + 2)^2 - (2x)^2
= (x^2 + 2 -2x)(x^2 + 2 +2x), using (A^2 - B^2) = (A - B)(A + B)
= (x^2 - 2x + 2)(x^2 + 2x +2) Ans. , using commutativity