Question

How do you factor `a^4+2a^2b^2+b^8`?

Answer 1

That expression is prime.

Explanation:

If you are certain about the exponent on b in the middle term, that expression is prime. That is to say, it does not factor.

However, `a^4+2a^2b^4+b^8` would be a Perfect Square Trinomial.
For `a^4+2a^2b^4+b^8`, we would observe that
the positive (principal) square root of
`a^4` is `a^2`, and the square root of `b^8` is `b^4`.
The middle term is twice the product of `a^2` and `b^4`.
Therefore we would have a Perfect Square Trinomial factoring as
`(a^2+b^4)^2`.