1. **State the problem:** Simplify the expression $$(2x+y)^2-(y-2x)^2$$. 2. **Formula used:** This is a difference of squares, which follows the rule $$a^2 - b^2 = (a-b)(a+b)$$. 3. **Apply the formula:** Let $$a = 2x + y$$ and $$b = y - 2x$$. 4. **Rewrite the expression:** $$ (2x+y)^2-(y-2x)^2 = ((2x+y)-(y-2x))((2x+y)+(y-2x)) $$ 5. **Simplify each factor:** First factor: $$ (2x+y)-(y-2x) = 2x + y - y + 2x = 4x $$ Second factor: $$ (2x+y)+(y-2x) = 2x + y + y - 2x = 2y $$ 6. **Multiply the simplified factors:** $$ 4x \times 2y = 8xy $$ 7. **Final answer:** $$ (2x+y)^2-(y-2x)^2 = 8xy $$