(4k²+2k+1)+(-4k²+2k-1)

To add these two polynomials, we simply combine like terms. Let's rearrange the terms to group them accordingly:

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

Now, we can simplify each group of terms:

(0) + (4k) + (0)

Therefore, the sum of the polynomials is 4k.