The expression \(175x^2 - 7y^2\) can be factored by factoring out the common factor of 7:

\[
175x^2 - 7y^2 = 7(25x^2 - y^2)
\]

Now, the term \(25x^2 - y^2\) is a difference of squares, which can be factored as:

\[
25x^2 - y^2 = (5x - y)(5x + y)
\]

Thus, the fully factored form of the expression is:

\[
175x^2 - 7y^2 = 7(5x - y)(5x + y)
\]

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

Here are 5 related questions:
1. How can you recognize a difference of squares in a polynomial?
2. What is the general formula for factoring a difference of squares?
3. Can you explain how common factors are factored out in algebraic expressions?
4. How would you factor \(49x^2 - 16y^2\)?
5. What happens when the polynomial cannot be factored further?

**Tip:** Always check for common factors first when factoring polynomials!

Learn how to factor the expression 175x^2 - 7y^2 by factoring out the common factor and applying the difference of squares. This detailed solution explores factoring techniques and algebraic concepts, making it suitable for students in Grades 9-10.

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