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

1 Answer
Apr 3, 2017

Answer:

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#.