(4k²+2k+1)+(-4k²+2k-1)

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

First, let's group the like terms together:

(4k² + (-4k²)) + (2k + 2k) + (1 + (-1))

Notice that the terms 4k² and -4k² cancel each other out, leaving us with:

0 + 4k + 0

Simplifying further, we have:

4k

So, the simplified expression is 4k.