1. **Problem:** Calculate the expression $a) (x - xy) \cdot (x^2 + y)$. 2. **Formula and rules:** Use distributive property: $ (A)(B + C) = AB + AC $ and factorization rules. 3. **Step-by-step solution:** - Expand $ (x - xy)(x^2 + y) = x(x^2 + y) - xy(x^2 + y) $ - Calculate each term: - $x \cdot x^2 = x^3$ - $x \cdot y = xy$ - $-xy \cdot x^2 = -x^3 y$ - $-xy \cdot y = -xy^2$ - Combine all terms: $$x^3 + xy - x^3 y - xy^2$$ - Group terms if possible: $$x^3 - x^3 y + xy - xy^2 = x^3(1 - y) + xy(1 - y)$$ - Factor out $(1 - y)$: $$(x^3 + xy)(1 - y)$$ 4. **Final answer:** $$ (x - xy)(x^2 + y) = (x^3 + xy)(1 - y) $$