(4k²+2k+1)+(-4k²+2k-1)

To add the two expressions:

(4k² + 2k + 1) + (-4k² + 2k - 1)

We can combine like terms. Starting with the k² terms:

4k² + (-4k²) = 0k² = 0

Next, let's combine the k terms:

2k + 2k = 4k

Finally, combining the constants:

1 + (-1) = 0

Putting it all together, the simplified expression is:

0k² + 4k + 0

Which can be further simplified to:

4k