Factorise 4x2−25 completely.

Sure, here is the step-by-step solution:

Step 1: Recognize the expression as a difference of squares. The difference of squares is a formula that can be used to factorise certain expressions, and it states that a² - b² = (a - b)(a + b).

Step 2: In the expression 4x² - 25, 4x² is (2x)² and 25 is 5². So, we can apply the difference of squares formula.

Step 3: Apply the formula. Replace a with 2x and b with 5.

Step 4: So, 4x² - 25 = (2x - 5)(2x + 5).

Therefore, the factorisation of 4x² - 25 is (2x - 5)(2x + 5).