1. **State the problem:** Simplify the expression $$d^2 (x + 2y) - b^2 (x + 2y)$$. 2. **Identify the common factor:** Both terms have the common factor $$(x + 2y)$$. 3. **Factor out the common term:** $$d^2 (x + 2y) - b^2 (x + 2y) = (x + 2y)(d^2 - b^2)$$ 4. **Recognize the difference of squares:** $$d^2 - b^2 = (d - b)(d + b)$$ 5. **Write the fully factored form:** $$ (x + 2y)(d - b)(d + b) $$ **Final answer:** $$d^2 (x + 2y) - b^2 (x + 2y) = (x + 2y)(d - b)(d + b)$$