(4k²+2k+1)+(-4k²+2k-1)

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

First, we'll combine the k² terms: 4k² + (-4k²) = 0.

Next, we'll combine the k terms: 2k + 2k = 4k.

Finally, we'll combine the constant terms: 1 + (-1) = 0.

Putting it all together, we have: 0 + 4k + 0.

So, the simplified expression is 4k.