1. **State the problem:** Simplify the expression $$(5-y)(2y-5)-(4-y)2$$. 2. **Use the distributive property (FOIL) to expand each product:** $$(5-y)(2y-5) = 5 \times 2y + 5 \times (-5) - y \times 2y - y \times (-5)$$ 3. **Calculate each term:** $$= 10y - 25 - 2y^2 + 5y$$ 4. **Simplify the second product:** $$(4-y)2 = 2 \times 4 - 2 \times y = 8 - 2y$$ 5. **Rewrite the original expression with expanded terms:** $$10y - 25 - 2y^2 + 5y - (8 - 2y)$$ 6. **Distribute the minus sign to the second group:** $$10y - 25 - 2y^2 + 5y - 8 + 2y$$ 7. **Combine like terms:** $$-2y^2 + (10y + 5y + 2y) + (-25 - 8) = -2y^2 + 17y - 33$$ **Final answer:** $$\boxed{-2y^2 + 17y - 33}$$