The expression \(5x^2 - 10\) is a quadratic expression with a common factor. We can simplify it by factoring out the greatest common factor (GCF). Here are the steps:

### Factoring the Expression

1. **Identify the GCF**: The greatest common factor of \(5x^2\) and \(-10\) is \(5\).

2. **Factor Out the GCF**: 
   \[
   5x^2 - 10 = 5(x^2 - 2)
   \]

Thus, the expression \(5x^2 - 10\) can be factored as \(5(x^2 - 2)\).

### Additional Notes

- \(x^2 - 2\) is a difference of squares, and it cannot be factored further using real numbers.

Would you like further details on this topic? Here are some related questions that might expand your understanding:

1. How do you factor quadratic expressions in general?
2. What are the differences between real and complex roots in quadratic equations?
3. How do you use the quadratic formula to solve quadratic equations?
4. What is the significance of factoring in simplifying expressions?
5. How can you apply factoring to solve real-world problems?
6. What is the difference between factoring and expanding expressions?
7. How do you identify common factors in polynomial expressions?
8. Can all quadratic expressions be factored?

**Tip**: Always look for a greatest common factor before attempting to factor more complex expressions!

Learn how to simplify and factor the expression 5x^2 - 10 with a step-by-step solution. This problem covers key algebraic concepts, including factoring quadratic expressions and identifying greatest common factors (GCF). Suitable for students in Grades 7-9.

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