Factorise 121−49w2 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 term used when you have two perfect squares that are being subtracted from each other. In this case, 121 is the square of 11 (since 1111 = 121) and 49w^2 is the square of 7w (since 7w7w = 49w^2).

Step 2: Apply the difference of squares formula. The difference of squares formula is a^2 - b^2 = (a - b)(a + b). In this case, a is 11 and b is 7w.

Step 3: Substitute a and b into the formula. This gives us (11 - 7w)(11 + 7w).

So, 121 - 49w^2 factorises to (11 - 7w)(11 + 7w).