(4k²+2k+1)+(-4k²+2k-1)

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

First, let's combine the terms that have the same exponent for k². The terms 4k² and -4k² will cancel each other out, as they have the same coefficient but opposite signs.

Next, let's combine the terms that have the same exponent for k. The terms 2k and 2k can be added together to give us 4k.

Finally, let's combine the constant terms. The terms 1 and -1 will cancel each other out.

Putting it all together, we have:

(4k²+2k+1)+(-4k²+2k-1) = 4k + 0

Simplified, the expression becomes 4k.