(4k²+2k+1)+(-4k²+2k-1)

To simplify the expression, we can combine like terms.

(4k² + 2k + 1) + (-4k² + 2k - 1)

Group the k² terms together and the k terms together:

(4k² - 4k²) + (2k + 2k) + (1 - 1)

Simplify each group:

0 + 4k + (0)

The final simplified expression is:

4k