Polynomial Factorization - from Expansion to factorization

Question

Using which identity or steps can I use to expand

y⁸ + 64

to

y⁸ + 4y⁶ + 8y⁴ - 4y⁶ - 16y⁴ - 32y² + 8y⁴ +32y² + 64

Is there a method I can use to find other factors?

Answer 1

All the middle terms cancel out, leaving y⁸ + 64.

You can factor as:

(y⁴ + 4y² + 8) * (y⁴ - 4y² + 8)

If you are allowed to use complex numbers, it can be factored more.