(4k²+2k+1)+(-4k²+2k-1)

To solve this expression, we need to simplify by combining like terms.

First, let's group the like terms:

(4k² + -4k²) + (2k + 2k) + (1 + -1)

The two terms with k² cancel each other out, so we're left with:

0k² + 4k + 0

The terms with k cancel each other out as well, so we're left with:

4k + 0

Finally, any number added to 0 is just the number itself, so we have:

4k

Therefore, (4k²+2k+1)+(-4k²+2k-1) simplifies to 4k.