(4k²+2k+1)+(-4k²+2k-1)

To add the given expressions, we need to combine like terms.

(4k² + 2k + 1) + (-4k² + 2k - 1)

Grouping together the terms with similar exponents of k, we have:

(4k² - 4k²) + (2k + 2k) + (1 - 1)

Simplifying further, we get:

0k² + 4k + 0

Since 0k² is just 0, we can simplify further:

0 + 4k + 0

Finally, we have:

4k + 0

Which can be written as simply:

4k