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

1 Answer
Apr 3, 2017

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.