1. **Problem:** Simplify the polynomial $(x + 2)(x + 7)$. 2. **Formula:** Use the distributive property (FOIL method) for binomials: $$(a + b)(c + d) = ac + ad + bc + bd$$ 3. **Apply FOIL:** $$x \cdot x + x \cdot 7 + 2 \cdot x + 2 \cdot 7 = x^2 + 7x + 2x + 14$$ 4. **Combine like terms:** $$x^2 + (7x + 2x) + 14 = x^2 + 9x + 14$$ 5. **Answer:** The simplified polynomial in standard form is $$x^2 + 9x + 14$$.