1. **Problem statement:** (a) Fully factorise $a^2 + 2ab + b^2 - 49$. 2. **Recall the formula:** The expression $a^2 + 2ab + b^2$ is a perfect square trinomial and can be written as $(a + b)^2$. 3. **Rewrite the expression:** $$a^2 + 2ab + b^2 - 49 = (a + b)^2 - 7^2$$ 4. **Use the difference of squares formula:** $$x^2 - y^2 = (x - y)(x + y)$$ where $x = a + b$ and $y = 7$. 5. **Apply the formula:** $$(a + b)^2 - 7^2 = ((a + b) - 7)((a + b) + 7)$$ 6. **Final factorised form:** $$(a + b - 7)(a + b + 7)$$ This is the fully factorised form of the given expression.