1. **State the problem:** Simplify the expression $-x \times 2y - xy \times -2x$. 2. **Recall multiplication rules:** When multiplying terms, multiply coefficients and variables separately. 3. **Simplify each term:** - First term: $-x \times 2y = -2xy$ - Second term: $xy \times -2x = -2x^2y$ 4. **Rewrite the expression:** $$-2xy - (-2x^2y)$$ 5. **Simplify the subtraction of a negative:** $$-2xy + 2x^2y$$ 6. **Factor common terms:** $$y(-2x + 2x^2)$$ 7. **Factor out $2x$ inside the parentheses:** $$y \times 2x(-1 + x)$$ 8. **Final simplified expression:** $$2xy(x - 1)$$