(4k²+2k+1)+(-4k²+2k-1)

To simplify the expression (4k²+2k+1)+(-4k²+2k-1), we will collect like terms:

First, let's combine the terms with k²:

4k² + (-4k²) = 0

Next, let's combine the terms with k:

2k + 2k = 4k

Finally, let's combine the constant terms:

1 + (-1) = 0

Therefore, the simplification of the expression is:

0 + 4k + 0

This can be further simplified as:

4k