1. **State the problem:** Multiply and simplify the expression $ (x + 3)(2x + 5) $. 2. **Recall the distributive property (FOIL method):** $ (a + b)(c + d) = ac + ad + bc + bd $ 3. **Apply FOIL to the given expression:** $$ (x + 3)(2x + 5) = x \cdot 2x + x \cdot 5 + 3 \cdot 2x + 3 \cdot 5 $$ 4. **Calculate each term:** $$ = 2x^2 + 5x + 6x + 15 $$ 5. **Combine like terms:** $$ 2x^2 + (5x + 6x) + 15 = 2x^2 + 11x + 15 $$ 6. **Final simplified expression:** $$ \boxed{2x^2 + 11x + 15} $$