The given expression is
x^2 - 121
This is a quadratic expression. To factorize, the first step is to multiply x^2 with
- 121. It becomes - 121x^2. We would find two terms such that their sum or difference is 0 and their product is - 121x^2. The terms are 11x and - 11x. By substituting 11x - 11x into the expression, it becomes
x^2 + 11x - 11x - 121
Factorize by grouping. It becomes
x(x + 11) - 11(x + 11)
(x + 11)(x - 11)
The result of the factorization is
(x + 11)(x - 11)