1. Statement of the problem: Simplify the expression $4a^2 - [3a^2 - b - (2a^2 + ab - 3b^2)]$. 2. Formula and rules: Use the distributive property $x - (y+z) = x - y - z$ and the rule $x - (y - z) = x - y + z$. 3. Remove the innermost parentheses and distribute the minus: Inside the brackets we have $3a^2 - b - (2a^2 + ab - 3b^2)$. Distribute the minus across the inner parentheses to get $3a^2 - b - 2a^2 - ab + 3b^2$. 4. Simplify like terms inside the brackets: Combine $3a^2 - 2a^2$ to get $a^2$. So the bracket simplifies to $a^2 - ab - b + 3b^2$. 5. Subtract the bracket from $4a^2$: $4a^2 - (a^2 - ab - b + 3b^2)$. Distribute the minus sign to obtain $4a^2 - a^2 + ab + b - 3b^2$. 6. Combine like terms: $4a^2 - a^2 = 3a^2$ so the expression becomes $3a^2 + ab + b - 3b^2$. 7. Optional factorization by grouping: Group as $(3a^2 + ab) + (b - 3b^2)$. Factor each group: $a(3a + b) + b(1 - 3b)$. 8. Final answer: $3a^2 + ab + b - 3b^2$.