1. **State the problem:** Simplify the expression $ (x^2y + x)(xy - 1) - 2x(x^2y^2 - 1) $. 2. **Use distributive property:** Expand each product. $$ (x^2y + x)(xy - 1) = x^2y \cdot xy - x^2y \cdot 1 + x \cdot xy - x \cdot 1 $$ $$ = x^3y^2 - x^2y + x^2y - x $$ Notice $- x^2y + x^2y$ cancels out. 3. **Simplify the first part:** $$ x^3y^2 - x $$ 4. **Expand the second part:** $$ - 2x(x^2y^2 - 1) = -2x \cdot x^2y^2 + 2x = -2x^3y^2 + 2x $$ 5. **Combine all terms:** $$ (x^3y^2 - x) + (-2x^3y^2 + 2x) = x^3y^2 - x - 2x^3y^2 + 2x $$ 6. **Group like terms:** $$ (x^3y^2 - 2x^3y^2) + (-x + 2x) = -x^3y^2 + x $$ 7. **Final simplified expression:** $$ \boxed{x - x^3y^2} $$ This is the simplified form of the original expression.