The given expression is:

\[
x^2 - y^2 + 2x - 2y
\]

This is not factorable directly as a whole expression. However, we can break it down into different parts. Notice that the first two terms resemble the difference of squares, which can be factored using the identity:

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

So, applying this to the first two terms:

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

Thus, the expression becomes:

\[
(x - y)(x + y) + 2x - 2y
\]

Next, we can factor out a common term from the remaining two terms \( 2x - 2y \):

\[
2(x - y)
\]

So, the entire expression is now:

\[
(x - y)(x + y) + 2(x - y)
\]

Finally, we can factor out \( (x - y) \) from both terms:

\[
(x - y) \left( (x + y) + 2 \right)
\]

Thus, the factored form of the expression is:

\[
(x - y)(x + y + 2)
\]

### Do you need more details or have any questions?

Here are 5 related questions for further exploration:
1. How do you factor higher-degree polynomials?
2. What are some common factoring techniques?
3. Can you use the difference of squares in a more complex equation?
4. How can factoring simplify solving equations?
5. What is the role of factoring in finding zeros of a function?

**Tip:** Always check for common factors before applying advanced factoring techniques.

Explore how to factor the algebraic expression x^2 - y^2 + 2x - 2y using the difference of squares and common factoring techniques. This problem focuses on key algebraic concepts such as factoring and is ideal for students in Grades 8-10.

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