Factor completely: x4 + 8x2 + 16

So assuming you know how to factor a normal quadratic formula, then you know that the first step is to multiply a times c and find the factors that add up to give you b. aXc (1X16) so you will be looking at factors of a positive 16.
1X16
2X8
4X4
Now the question is, "which one adds up to b?" The answer would be 4X4. Since you now know this, you can separate the quadratic into two parts. 
*****Since the first x is to the fourth power both middle values will be to the second power.
(x^4+4x^2)(4x^2+16)
Then take out a GCF from each. Remember you want what is in the parenthesis to end up being the same.
x^2(x^2+4) +4(x^2+4)
Then simplify the expression
(x^2+4)(x^2+4)
You can see that they are the same, so now you can condense it inot a final answer of:
(x^2+4)^2

Hope this helps! Let me know if you still have questions.