1. **Problem statement:** Factorise the expression given (assuming a general quadratic expression for demonstration, e.g., $x^2 + 5x + 6$). 2. **Formula and rules:** To factorise a quadratic expression of the form $ax^2 + bx + c$, find two numbers that multiply to $ac$ and add to $b$. 3. **Step-by-step factorisation:** - For $x^2 + 5x + 6$, find two numbers that multiply to $6$ and add to $5$. These numbers are $2$ and $3$. - Rewrite the middle term: $x^2 + 2x + 3x + 6$. - Group terms: $(x^2 + 2x) + (3x + 6)$. - Factor each group: $x(x + 2) + 3(x + 2)$. - Factor out the common binomial: $(x + 2)(x + 3)$. 4. **Explanation:** We split the middle term to create two binomials that share a common factor, allowing us to factorise the expression fully. 5. **Final answer:** The factorised form is $$(x + 2)(x + 3)$$.