(4k²+2k+1)+(-4k²+2k-1)

To simplify the expression, we can combine like terms:

(4k² + 2k + 1) + (-4k² + 2k - 1)

Combine the k² terms: 4k² + (-4k²) = 0

Combine the k terms: 2k + 2k = 4k

Combine the constant terms: 1 + (-1) = 0

Putting it all together, we have:

0 + 4k + 0

Simplifying further:

4k