1: \(\left(2x+1\right)^2+\left(2x-1\right)^2\)

\(=4x^2+4x+1+4x^2-4x+1\)

\(=8x^2+2\)

2: \(-\left(x+1\right)^2-\left(x-1\right)^2\)

\(=-\left(x^2+2x+1\right)-\left(x^2-2x+1\right)\)

\(=-x^2-2x-1-x^2+2x-1\)

\(=-2x^2-2\)

3: \(\left(x+2y\right)^2-\left(x-2y\right)^2\)

\(=\left(x+2y+x-2y\right)\left(x+2y-x+2y\right)\)

\(=2x\cdot4y=8xy\)