1. **State the problem:** Factorise the expression $$16 - 25(b+3)^2$$. 2. **Identify the formula:** This expression is a difference of squares, which follows the formula $$a^2 - b^2 = (a - b)(a + b)$$. 3. **Rewrite the terms as squares:** $$16 = 4^2$$ $$25(b+3)^2 = (5(b+3))^2$$ 4. **Apply the difference of squares formula:** $$16 - 25(b+3)^2 = 4^2 - (5(b+3))^2 = (4 - 5(b+3))(4 + 5(b+3))$$ 5. **Expand the factors:** $$(4 - 5(b+3)) = 4 - 5b - 15 = -5b - 11$$ $$(4 + 5(b+3)) = 4 + 5b + 15 = 5b + 19$$ 6. **Final factorised form:** $$16 - 25(b+3)^2 = (-5b - 11)(5b + 19)$$ This is the fully factorised expression.