Factorise 9w2−49 completely.

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

Step 1: Recognize that the given expression is a difference of squares. The difference of squares is a term used to describe expressions in the form a² - b², which can be factored into (a - b)(a + b).

Step 2: In the expression 9w² - 49, 9w² is a square (since (3w)² = 9w²) and 49 is also a square (since 7² = 49).

Step 3: Therefore, we can write the expression as (3w)² - 7².

Step 4: Now, apply the difference of squares formula. This gives us (3w - 7)(3w + 7).

So, the factorization of 9w² - 49 is (3w - 7)(3w + 7).