(4k²+2k+1)+(-4k²+2k-1)

To simplify the expression, we can combine like terms.

(4k² + 2k + 1) + (-4k² + 2k - 1)

First, let's combine the terms that have k²:

4k² + (-4k²) = 0 (since positive 4k² and negative 4k² cancel each other out)

Next, let's combine the terms that have k:

2k + 2k = 4k

Lastly, let's combine the constant terms:

1 + (-1) = 0

Putting it all together, the simplified expression is:

0 + 4k + 0

Which simplifies to just 4k.