(4k²+2k+1)+(-4k²+2k-1)

To add these two expressions:

(4k² + 2k + 1) + (-4k² + 2k - 1)

First, you can combine like terms.

The terms with k² on both sides cancel each other out: 4k² - 4k² = 0.

Then, you can combine the terms with k:

2k + 2k = 4k.

Finally, you can add the constant terms:

1 + (-1) = 0.

Therefore, the simplified expression is:

4k + 0 = 4k.