1. **State the problem:** Factorise completely the expression $$(c + d)^2 - d^2$$. 2. **Recall the formula:** This expression is a difference of squares, which follows the identity: $$a^2 - b^2 = (a - b)(a + b)$$ where $a = c + d$ and $b = d$. 3. **Apply the formula:** $$ (c + d)^2 - d^2 = ((c + d) - d)((c + d) + d) $$ 4. **Simplify each factor:** $$ ((c + d) - d) = c $$ $$ ((c + d) + d) = c + 2d $$ 5. **Write the fully factorised form:** $$ c(c + 2d) $$ This matches the given handwritten formula, confirming the factorisation is correct. **Final answer:** $$c(c + 2d)$$