Factorise 81−25m2 completely.

Sure, let's factorise the expression 81−25m^2 step by step.

Step 1: Recognise the expression as a difference of squares. The difference of squares is a term used in algebra to describe the difference between two squared numbers. The formula for factoring the difference of squares is a^2 - b^2 = (a - b)(a + b).

Step 2: In our case, 81 is the square of 9 (since 99 = 81) and 25m^2 is the square of 5m (since 5m5m = 25m^2). So we can rewrite the expression as (9)^2 - (5m)^2.

Step 3: Apply the difference of squares formula. Replace 'a' with 9 and 'b' with 5m in the formula (a - b)(a + b).

Step 4: So, 81 - 25m^2 = (9 - 5m)(9 + 5m).

So, the expression 81−25m^2 factorises to (9 - 5m)(9 + 5m).