(4k²+2k+1)+(-4k²+2k-1)

To add the two expressions (4k² + 2k + 1) and (-4k² + 2k - 1), you simply combine like terms.

First, let's add the like terms: 4k² + (-4k²) = 0

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

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

Putting it all together, the sum is: 0 + 4k + 0

Therefore, the final expression is 4k.