1. **State the problem:** Factorise the expression $18a^2 - 98$. 2. **Identify common factors:** Both terms have a common factor of 2. 3. **Factor out the common factor:** $$18a^2 - 98 = 2(9a^2 - 49)$$ 4. **Recognize the difference of squares:** $$9a^2 - 49 = (3a)^2 - 7^2$$ 5. **Apply the difference of squares formula:** $$x^2 - y^2 = (x - y)(x + y)$$ 6. **Factor the expression inside the parentheses:** $$9a^2 - 49 = (3a - 7)(3a + 7)$$ 7. **Write the fully factorised form:** $$18a^2 - 98 = 2(3a - 7)(3a + 7)$$ **Final answer:** $2(3a - 7)(3a + 7)$