1. **Problem:** Factorise the expression $25x^2 - 36$. 2. **Formula:** Use the difference of squares formula: $$a^2 - b^2 = (a - b)(a + b)$$ 3. **Identify terms:** Here, $25x^2 = (5x)^2$ and $36 = 6^2$. 4. **Apply formula:** $$25x^2 - 36 = (5x)^2 - 6^2 = (5x - 6)(5x + 6)$$ 5. **Explanation:** The difference of squares formula allows us to factor expressions where two perfect squares are subtracted. We write each term as a square and then express the original expression as the product of the sum and difference of their square roots. **Final answer:** $(5x - 6)(5x + 6)$