Докажите тождество: (x+2y)^2-(x-2y)^2=8xy.

\[(x + 2y)^{2} - (x - 2y)^{2} = 8xy\]

\[(x + 2y + x - 2y)(x + 2y - x + 2y) = 8xy\]

\[2x \cdot 4y = 8xy\]

\[8xy = 8xy.\]

\[Тождество\ доказано.\]