1. **Stating the problem:** Simplify the algebraic expression: $$2a \cdot (-3b) + (-3a^2) \cdot (-4b) - 4a^2b$$ and $$\frac{-4ab^2 \cdot (3a^2b) - 2a^2b^2 \cdot (-5ab^2) - 2a^4b^4}{1}$$ 2. **Formula and rules:** Use the distributive property and multiplication of powers with the same base: $$a^m \cdot a^n = a^{m+n}$$ 3. **Step-by-step simplification of the first expression:** $$2a \cdot (-3b) = -6ab$$ $$(-3a^2) \cdot (-4b) = 12a^2b$$ So the expression becomes: $$-6ab + 12a^2b - 4a^2b$$ Combine like terms $12a^2b - 4a^2b$: $$12a^2b - 4a^2b = (12 - 4)a^2b = 8a^2b$$ Final simplified form: $$-6ab + 8a^2b$$ 4. **Step-by-step simplification of the second expression numerator:** Calculate each product: $$-4ab^2 \cdot 3a^2b = -4 \cdot 3 \cdot a^{1+2} \cdot b^{2+1} = -12a^3b^3$$ $$-2a^2b^2 \cdot (-5ab^2) = -2 \cdot (-5) \cdot a^{2+1} \cdot b^{2+2} = 10a^3b^4$$ $$-2a^4b^4$$ (remains as is) So the numerator is: $$-12a^3b^3 + 10a^3b^4 - 2a^4b^4$$ Since the denominator is 1, the expression is: $$-12a^3b^3 + 10a^3b^4 - 2a^4b^4$$ 5. **Final answers:** First expression simplified: $$\boxed{-6ab + 8a^2b}$$ Second expression simplified: $$\boxed{-12a^3b^3 + 10a^3b^4 - 2a^4b^4}$$