(4k²+2k+1)+(-4k²+2k-1)

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

Like terms are the terms that have the same variable raised to the same exponent. In this case, the like terms are the terms with the variable k raised to the power of 2 and the terms with just the variable k.

The variable k²: (4k² + (-4k²)) = 0

The variable k: (2k + 2k) = 4k

The constant term: (1 + (-1)) = 0

Therefore, the simplified expression is 0 + 4k + 0, which simplifies to just 4k.