## Factoring a Quadratic Expression: (x + 2y - 3)^2 - 4(x + 2y - 3) + 4

This expression might look complicated at first glance, but it can be simplified by recognizing a pattern and using algebraic techniques.

### Identifying the Pattern

Notice that the expression has the following structure:

**(something)^2 - 4(something) + 4**

This structure strongly resembles the pattern of a **perfect square trinomial**:

**(a - b)^2 = a^2 - 2ab + b^2**

### Applying the Pattern

Let's identify the 'a' and 'b' terms in our expression:

**a = (x + 2y - 3)****b = 2**

Now, we can rewrite the expression using the perfect square trinomial pattern:

**(x + 2y - 3)^2 - 4(x + 2y - 3) + 4 = (x + 2y - 3 - 2)^2**

### Simplifying the Expression

Finally, simplify the expression:

**(x + 2y - 3 - 2)^2 = (x + 2y - 5)^2**

### Conclusion

By recognizing the pattern of a perfect square trinomial, we were able to factor the given expression and simplify it to **(x + 2y - 5)^2**.