(4k²+2k+1)+(-4k²+2k-1)

To add the two given expressions, we can simply combine like terms.

(4k²+2k+1)+(-4k²+2k-1) = 4k²+2k+1-4k²+2k-1

Now let's group the like terms together:

(4k²-4k²) + (2k+2k) + (1-1)

The first group, 4k²-4k², is equal to 0, so it disappears.

The second group, 2k+2k, is equal to 4k.

The third group, 1-1, is equal to 0, so it disappears.

Therefore, the simplified expression is:

4k.