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Factor a^{2} - 121 b^{2}

In this term, we're going to factor it by using DOTS or the difference of two squares. 

We must always remember that DOTS consist of the following:

The first and second terms should be a perfect square;
The sign of the second term should always be negative (-).

 a^{2} -  b^{2} = (a - b)(a + b)

So back to the given...

 a^{2} - 121b^{2}

The first and the second term are perfect squares so the next step is to find their square roots; so, 

The answer is: (a - 11b) (a + 11b)