(4k²+2k+1)+(-4k²+2k-1)

To add the two expressions, we need to combine the like terms.

Starting with the k^2 terms: 4k^2 + (-4k^2) = 0k^2

Next, the k terms: 2k + 2k = 4k

Finally, the constant terms: 1 + (-1) = 0

Putting it all together, the sum of (4k² + 2k + 1) and (-4k² + 2k - 1) is: 0k^2 + 4k + 0 which simplifies to 4k.