1. **State the problem:** Fully factorise the expression $3k^2 + 9k$. 2. **Identify common factors:** Both terms have a common factor of 3 and $k$. 3. **Factor out the greatest common factor (GCF):** $$3k^2 + 9k = 3k(k + 3)$$ 4. **Check if further factorisation is possible:** The binomial $k + 3$ cannot be factored further. 5. **Final answer:** $$3k(k + 3)$$ This is the fully factorised form of the expression.