1. State the problem: Fully factorise the cubic expression $$x^3 - 25x$$. 2. Factor out the common factor: Both terms have a common factor of $$x$$, so factor it out: $$x^3 - 25x = x(x^2 - 25)$$. 3. Recognize the difference of squares: The expression inside the parentheses is a difference of squares since $$25 = 5^2$$, so apply the formula $$a^2 - b^2 = (a - b)(a + b)$$: $$x(x^2 - 25) = x(x - 5)(x + 5)$$. 4. Final factorised form is: $$x(x - 5)(x + 5)$$.