https://file.aiquickdraw.com/mathbot/file/17266735616990u54u099.jpg

The given expression is \( 25x^2 - 16 \).

This is a difference of squares, which follows the pattern:

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

Here, we can rewrite \( 25x^2 \) as \( (5x)^2 \) and \( 16 \) as \( 4^2 \). Therefore, the expression becomes:

\[
25x^2 - 16 = (5x)^2 - 4^2
\]

Now apply the difference of squares formula:

\[
25x^2 - 16 = (5x - 4)(5x + 4)
\]

Thus, the completely factored form of \( 25x^2 - 16 \) is:

\[
(5x - 4)(5x + 4)
\]

Would you like more details on any part of this solution? 

Here are 5 related questions to extend this concept:
1. How would you factor the expression \( 9x^2 - 25 \)?
2. Can every quadratic expression be factored using the difference of squares method?
3. What is the factored form of \( 4x^2 - 49 \)?
4. How do you determine if an expression is a difference of squares?
5. What happens when you try to factor \( x^2 + 4 \), which is a sum of squares?

**Tip:** Always check for the greatest common factor (GCF) before applying other factoring methods!

Explore how to factor the quadratic expression 25x^2 - 16 using the difference of squares formula. This step-by-step guide covers essential algebra concepts, suitable for students in Grades 9-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation