Question

Factor COMPLETELY over the complex numbers, if possible: a4 - b4

Answer 1

$a^4-b^4=(a^2)^2-(b^2)^2=(a^2-b^2)(a^2+b^2)$

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

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

$a^4-b^4=(a-b)(a+b)(a-ib)(a+ib)$