To factor the expression \(3x^2 - 125\), follow these steps:

1. Notice that the expression is a difference of squares. A difference of squares has the general form \(a^2 - b^2 = (a + b)(a - b)\).

2. First, rewrite the expression in a form that clearly shows the difference of squares:

   \[
   3x^2 - 125 = \sqrt{3}x^2 - \sqrt{125}^2
   \]

3. Recognize that the expression can be written as:

   \[
   3x^2 - 125 = \left(\sqrt{3}x\right)^2 - \left(\sqrt{125}\right)^2
   \]

4. Now, apply the difference of squares formula:

   \[
   \left(\sqrt{3}x\right)^2 - \left(\sqrt{125}\right)^2 = \left(\sqrt{3}x + \sqrt{125}\right)\left(\sqrt{3}x - \sqrt{125}\right)
   \]

So, the factored form of \(3x^2 - 125\) is:

\[
(\sqrt{3}x + 5\sqrt{5})(\sqrt{3}x - 5\sqrt{5})
\]

Would you like more details or have any questions?

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Here are five related questions:
1. How do you factor the sum of squares?
2. Can you factor \(x^2 - 49\)?
3. What is the difference between perfect square trinomials and the difference of squares?
4. How do you solve quadratic equations by factoring?
5. Can the expression \(3x^2 + 125\) be factored similarly?

**Tip:** Always check if an expression can be simplified before factoring, especially when dealing with quadratic expressions.

Understand how to factor the quadratic expression 3x^2 - 125 by applying the difference of squares method. This step-by-step solution involves recognizing the structure of the expression and using key algebraic formulas. Ideal for high school students studying algebra.

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