Factoring and Foiling out

Question

a⁴ + 1 (have to be foil out too)

a⁴ – 64

Answer 1

a^4 + 1 has no real factors.

It may be factored as (a + (√2 + √2i)/2) (a + (√2 - √2i)/2)(a - (√2 + √2i)/2) (a - (√2 - √2i)/2)

If you'd like, you may write the factoring as (a^2 + √2a + 1) (a^2 - √2a + 1)

a^4 - 64 = (a^2 + 8)(a^2 - 8) = (a^2 + 8)(a + 2√2)(a - 2√2)

If imaginary solutions are accepted, this factors as (a + 2√2i)(a - 2√2i)(a + 2√2)(a - 2√2)