1. **State the problem:** Factorise the expression $2y + 8yz$. 2. **Identify common factors:** Look for the greatest common factor (GCF) in both terms. Here, both terms have a factor of $2y$. 3. **Apply the distributive property:** Factor out $2y$ from each term: $$2y + 8yz = 2y(1) + 2y(4z) = 2y(1 + 4z)$$ 4. **Final answer:** The factorised form is $$2y(1 + 4z)$$. This means the original expression can be rewritten as the product of $2y$ and the binomial $(1 + 4z)$.