1. **State the problem:** Expand and simplify the expression $$(x + 7)(x - 2)$$. 2. **Formula used:** Use the distributive property (also called FOIL for binomials): $$ (a + b)(c + d) = ac + ad + bc + bd $$ 3. **Apply the formula:** $$ (x + 7)(x - 2) = x \cdot x + x \cdot (-2) + 7 \cdot x + 7 \cdot (-2) $$ 4. **Calculate each term:** $$ = x^2 - 2x + 7x - 14 $$ 5. **Combine like terms:** $$ = x^2 + ( -2x + 7x ) - 14 $$ $$ = x^2 + 5x - 14 $$ 6. **Final answer:** $$ \boxed{x^2 + 5x - 14} $$