1. **State the problem:** Factorise the expression $ab^2 + a^2b$. 2. **Identify common factors:** Both terms contain the variables $a$ and $b$. 3. **Extract the greatest common factor (GCF):** The smallest power of $a$ is $a^1$ and the smallest power of $b$ is $b^1$, so the GCF is $ab$. 4. **Factor out the GCF:** $$ab^2 + a^2b = ab(b) + ab(a) = ab(b + a)$$ 5. **Final answer:** The factorised form is $$ab(a + b)$$ This means the original expression can be written as the product of $ab$ and the sum $(a + b)$.