1. **Problem:** Factorise the expression $3x^2 - 48$. 2. **Formula and rules:** - To factorise expressions like this, look for a common factor first. - Then check if the remaining expression is a difference of squares, which factors as $$a^2 - b^2 = (a - b)(a + b)$$. 3. **Step-by-step solution:** 1. Identify the common factor in $3x^2$ and $48$. Both terms are divisible by 3. 2. Factor out 3: $$3x^2 - 48 = 3(x^2 - 16)$$ 3. Recognize that $x^2 - 16$ is a difference of squares since $16 = 4^2$. 4. Apply the difference of squares formula: $$x^2 - 16 = (x - 4)(x + 4)$$ 5. Substitute back: $$3(x - 4)(x + 4)$$ 4. **Final answer:** $$3(x - 4)(x + 4)$$ This is the fully factorised form of $3x^2 - 48$. You can check by expanding to verify it equals the original expression.