(4k²+2k+1)+(-4k²+2k-1)

To simplify the expression (4k²+2k+1)+(-4k²+2k-1), we need to combine like terms.

First, let's add the terms with the same degree of k²: 4k² + (-4k²) = 0k² = 0

Next, let's add the terms with the same degree of k: 2k + 2k = 4k

Lastly, let's add the constant terms: 1 + (-1) = 0

Putting it all together, we have: (4k²+2k+1)+(-4k²+2k-1) = 0k² + 4k + 0 Simplified: 4k