Factorise 64m2−1 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 pattern in algebra where the difference between two squares can be factored into the product of the sum and difference of the two terms. The general form is a² - b² = (a - b)(a + b).

Step 2: In the given expression 64m² - 1, 64m² is a perfect square (because (8m)² = 64m²) and 1 is also a perfect square (because 1² = 1).

Step 3: Apply the difference of squares formula. Let a = 8m and b = 1. Then, the expression 64m² - 1 can be factored as (8m - 1)(8m + 1).

So, the factorization of 64m² - 1 is (8m - 1)(8m + 1).