Factorise 25x2−9 completely.

Sure, let's factorise the given expression step by step.

The given expression is 25x^2 - 9.

This is a difference of squares, which can be factorised as follows:

A difference of squares is an expression of the form a^2 - b^2 and it can be factorised as (a - b)(a + b).

Here, 25x^2 is (5x)^2 and 9 is 3^2.

So, we can write 25x^2 - 9 as (5x)^2 - 3^2.

Therefore, by applying the difference of squares formula, we get:

25x^2 - 9 = (5x - 3)(5x + 3).

So, the factorisation of 25x^2 - 9 is (5x - 3)(5x + 3).