(4k²+2k+1)+(-4k²+2k-1)

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

= 4k² + 2k + 1 - 4k² + 2k - 1

Next, we can group the like terms together:

= (4k² - 4k²) + (2k + 2k) + (1 - 1)

The terms with k² cancel each other out, leaving us with:

= 0 + 4k + 0

Simplifying further:

= 4k

Therefore, the simplified expression is 4k.