1. **State the problem:** Simplify the expression $$4a^2 - [3a^2 - b - (2a^2 + ab - 3b^2)]$$. 2. **Understand the rules:** When simplifying expressions with brackets, start from the innermost brackets and work outward. Remember to distribute the minus sign when removing brackets. 3. **Simplify the innermost bracket:** $$3a^2 - b - (2a^2 + ab - 3b^2) = 3a^2 - b - 2a^2 - ab + 3b^2$$ 4. **Combine like terms inside the bracket:** $$3a^2 - 2a^2 = a^2$$ So the expression becomes: $$a^2 - b - ab + 3b^2$$ 5. **Rewrite the original expression:** $$4a^2 - [a^2 - b - ab + 3b^2]$$ 6. **Distribute the minus sign across the bracket:** $$4a^2 - a^2 + b + ab - 3b^2$$ 7. **Combine like terms:** $$4a^2 - a^2 = 3a^2$$ 8. **Final simplified expression:** $$3a^2 + ab + b - 3b^2$$