(4k²+2k+1)+(-4k²+2k-1)

To add the two expressions (4k²+2k+1) and (-4k²+2k-1), we can simply combine like terms.

The like terms are: 4k² and -4k² (coefficient of k²) 2k and 2k (coefficient of k) 1 and -1 (constant term)

When combining the like terms, we add the coefficients:

4k² + (-4k²) = 0 2k + 2k = 4k 1 + (-1) = 0

Therefore, the sum of the two expressions is: 0 + 4k + 0, which can be simplified as 4k.