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

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, ${a}^{4} + 2 {a}^{2} {b}^{4} + {b}^{8}$ would be a Perfect Square Trinomial.
For ${a}^{4} + 2 {a}^{2} {b}^{4} + {b}^{8}$, 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
${\left({a}^{2} + {b}^{4}\right)}^{2}$.