To factor the quadratic expression \( 25x^2 - 144 \), we can recognize it as a difference of squares.

The difference of squares formula is: 
\[ a^2 - b^2 = (a + b)(a - b) \]

In this case:
\[ 25x^2 - 144 \]

First, we identify \( a \) and \( b \):
\[ 25x^2 = (5x)^2 \]
\[ 144 = 12^2 \]

So, we rewrite the expression using the difference of squares formula:
\[ 25x^2 - 144 = (5x)^2 - 12^2 = (5x + 12)(5x - 12) \]

Thus, the factored form of \( 25x^2 - 144 \) is:
\[ (5x + 12)(5x - 12) \]

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

Here are 5 relative questions to consider:
1. What is the difference of squares formula?
2. How do you identify \( a \) and \( b \) in a difference of squares?
3. Can all quadratic expressions be factored using the difference of squares?
4. What happens if \( 25x^2 - 144 \) was a sum of squares instead?
5. How can the factored form be used to solve for the roots of the equation \( 25x^2 - 144 = 0 \)?

**Tip:** The difference of squares can only be applied when you have a subtraction between two perfect squares.

Learn how to factorize 25x^2 - 144 using the difference of squares formula. This problem involves recognizing perfect squares, applying the difference of squares formula, and solving quadratic expressions. Suitable for high school students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation