1. **Problem statement:** Factorise the quadratic expressions given. 2. **Formula and rules:** To factorise a quadratic expression of the form $x^2 + bx + c$, find two numbers that multiply to $c$ and add to $b$. 3. **Part a) $x^2 + 13x + 42$** - Find two numbers that multiply to 42 and add to 13: 6 and 7. - So, $x^2 + 13x + 42 = (x + 6)(x + 7)$. 4. **Part b) $x^2 - 4x + 4$** - Find two numbers that multiply to 4 and add to -4: -2 and -2. - So, $x^2 - 4x + 4 = (x - 2)(x - 2) = (x - 2)^2$. 5. **Part c) $x^2 - 2x - 48$** - Find two numbers that multiply to -48 and add to -2: 6 and -8. - So, $x^2 - 2x - 48 = (x + 6)(x - 8)$. 6. **Part d) $x^2 + 5x - 6$** - Find two numbers that multiply to -6 and add to 5: 6 and -1. - So, $x^2 + 5x - 6 = (x + 6)(x - 1)$. **Final answers:** - a) $(x + 6)(x + 7)$ - b) $(x - 2)^2$ - c) $(x + 6)(x - 8)$ - d) $(x + 6)(x - 1)$