1. **State the problem:** Simplify the expression $ (a - b)^2 - 3b(2b - a) $. 2. **Recall formulas and rules:** - The square of a binomial: $ (x - y)^2 = x^2 - 2xy + y^2 $ - Distributive property: $ a(b + c) = ab + ac $ 3. **Expand the first term:** $$ (a - b)^2 = a^2 - 2ab + b^2 $$ 4. **Expand the second term:** $$ -3b(2b - a) = -3b \times 2b + (-3b) \times (-a) = -6b^2 + 3ab $$ 5. **Rewrite the expression with expansions:** $$ a^2 - 2ab + b^2 - 6b^2 + 3ab $$ 6. **Combine like terms:** $$ a^2 + (-2ab + 3ab) + (b^2 - 6b^2) = a^2 + ab - 5b^2 $$ 7. **Final simplified expression:** $$ \boxed{a^2 + ab - 5b^2} $$