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To factor the expression \( 25x^2 - 144 \) completely, we can use the difference of squares formula, which is:

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

In this case:

1. Recognize that \( 25x^2 \) and \( 144 \) are both perfect squares.
   - \( 25x^2 = (5x)^2 \)
   - \( 144 = 12^2 \)

2. Rewrite the expression as a difference of squares:
   \[
   25x^2 - 144 = (5x)^2 - 12^2
   \]

3. Apply the difference of squares formula:
   \[
   (5x)^2 - 12^2 = (5x + 12)(5x - 12)
   \]

So, the fully factored form of \( 25x^2 - 144 \) is:

\[
(5x + 12)(5x - 12)
\]

Would you like further details or have any questions?

Here are five related questions to expand on this topic:

1. How do you recognize when an expression is a difference of squares?
2. What are other common factoring techniques besides the difference of squares?
3. Can the expression \( 25x^2 - 144 \) be factored further?
4. What are examples of binomials that cannot be factored as a difference of squares?
5. How does factoring help in solving quadratic equations?

**Tip:** When factoring a difference of squares, always check if both terms are perfect squares. This is key to quickly identifying the factors.

Factor the following binomial completely: 25x^2 - 144.

Learn how to factor the binomial 25x^2 - 144 completely by applying the difference of squares formula. This solution explains key algebra concepts and step-by-step factoring, ideal for students in Grades 8-10.

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