https://file.aiquickdraw.com/mathbot/file/1727846923281pqkoynyf.jpg

The expression in the image is:

\[
\frac{x^2 - y^2}{x - y}
\]

This is a difference of squares, which can be factored as follows:

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

Thus, the expression becomes:

\[
\frac{(x - y)(x + y)}{x - y}
\]

Since \(x - y \neq 0\), we can cancel out the common term \(x - y\) from the numerator and the denominator:

\[
x + y
\]

Therefore, the simplified expression is:

\[
x + y
\]

Would you like more details or have any questions about this?

Here are 5 related questions you might find useful:
1. What happens if \(x = y\) in the original expression?
2. How do we factor other types of polynomials similar to \(x^2 - y^2\)?
3. Can the difference of cubes, \(x^3 - y^3\), be factored in a similar way?
4. How do you apply factoring techniques in solving equations?
5. What is the importance of factoring in calculus, particularly for simplifying limits?

**Tip:** When simplifying expressions, always check for common factors in both the numerator and denominator that can be canceled out!

Simplify the expression \(\frac{x^2 - y^2}{x - y}\).

Learn how to simplify the expression \(\frac{x^2 - y^2}{x - y}\) by factoring the difference of squares. This step-by-step solution is perfect for students learning factoring techniques in Grades 8-10.

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