(4k²+2k+1)+(-4k²+2k-1)

To simplify the expression (4k²+2k+1)+(-4k²+2k-1), we can combine like terms.

First, we can combine the two terms that have a coefficient of 4k²: (4k² + 2k + 1) + (-4k² + 2k - 1) = 4k² + (-4k²) + 2k + 2k + 1 + (-1)

The corresponding terms with a coefficient of 4k² and -4k² cancel each other out: = (4k² - 4k²) + (2k + 2k) + (1 - 1) = 0 + 4k + 0 = 4k

Therefore, the simplified expression is 4k.