1. **State the problem:** Simplify the expression $$(x - 1) \cdot x^2 + 3 \cdot (x - 3)^2$$. 2. **Recall formulas and rules:** - Use distributive property: $a(b + c) = ab + ac$. - Expand powers: $(a - b)^2 = a^2 - 2ab + b^2$. 3. **Expand each term:** - First term: $(x - 1) \cdot x^2 = x \cdot x^2 - 1 \cdot x^2 = x^3 - x^2$. - Second term: $3 \cdot (x - 3)^2 = 3 \cdot (x^2 - 2 \cdot 3 \cdot x + 3^2) = 3 \cdot (x^2 - 6x + 9)$. 4. **Distribute 3 in the second term:** $$3 \cdot x^2 - 3 \cdot 6x + 3 \cdot 9 = 3x^2 - 18x + 27$$ 5. **Combine all terms:** $$x^3 - x^2 + 3x^2 - 18x + 27$$ 6. **Simplify like terms:** $$x^3 + ( - x^2 + 3x^2 ) - 18x + 27 = x^3 + 2x^2 - 18x + 27$$ **Final answer:** $$x^3 + 2x^2 - 18x + 27$$