The given expression is:

\[
y^2 - 121(a-b)^2
\]

We recognize that this is a difference of squares, which follows the general form:

\[
x^2 - z^2 = (x - z)(x + z)
\]

Here, \(x = y\) and \(z = 11(a - b)\) because \(121 = 11^2\). So, we can apply the difference of squares formula:

\[
y^2 - (11(a - b))^2 = (y - 11(a - b))(y + 11(a - b))
\]

Thus, the factorization of the expression is:

\[
(y - 11(a - b))(y + 11(a - b))
\]

Would you like more explanation on the difference of squares, or have any other questions on this? Here's a list of related questions for you:

1. How do you factorize other types of polynomials?
2. Can you explain the difference of squares in more detail?
3. How does factoring help solve algebraic equations?
4. What happens when the expression involves cubes instead of squares?
5. How do you expand factored expressions back out?

**Tip:** Recognizing patterns like the difference of squares can speed up factoring and simplify complex expressions.

Learn how to factorize the expression y^2 - 121(a-b)^2 using the difference of squares method. This solution explains how to recognize patterns and apply the formula for factoring a difference of squares. Suitable for students in Grades 8-10.

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