1. **State the problem:** Simplify the expression $$-(3ab + b^2 - 5a^2 b) + (a^2 - 5ab + 2b^2) - (a^2 b - 3a^2 + b^2)$$. 2. **Remove parentheses carefully, applying signs:** $$-(3ab + b^2 - 5a^2 b) = -3ab - b^2 + 5a^2 b$$ $$-(a^2 b - 3a^2 + b^2) = -a^2 b + 3a^2 - b^2$$ So the expression becomes: $$-3ab - b^2 + 5a^2 b + a^2 - 5ab + 2b^2 - a^2 b + 3a^2 - b^2$$ 3. **Group like terms:** - Terms with $a^2 b$: $5a^2 b - a^2 b = 4a^2 b$ - Terms with $ab$: $-3ab - 5ab = -8ab$ - Terms with $b^2$: $-b^2 + 2b^2 - b^2 = 0$ - Terms with $a^2$: $a^2 + 3a^2 = 4a^2$ 4. **Write the simplified expression:** $$4a^2 b - 8ab + 4a^2$$ 5. **Factor if possible:** Factor out $4a$: $$4a( a b - 2b + a )$$ This is the simplified form. **Final answer:** $$4a^2 b - 8ab + 4a^2 = 4a( a b - 2b + a )$$