Question
Factor. \[ 9-25 w^{2} \] \( \square \square \square \)
Ask by Long French. in the United States
Jan 27,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\[
(3 - 5w)(3 + 5w)
\]
Solution
To factor the expression \( 9 - 25w^{2} \), you can recognize it as a **difference of squares**. The difference of squares formula is:
\[
a^{2} - b^{2} = (a - b)(a + b)
\]
Here's how you can apply this to your expression:
1. **Identify \( a \) and \( b \):**
- \( 9 \) is a perfect square and can be written as \( 3^{2} \).
- \( 25w^{2} \) is also a perfect square and can be written as \( (5w)^{2} \).
2. **Apply the difference of squares formula:**
\[
9 - 25w^{2} = 3^{2} - (5w)^{2} = (3 - 5w)(3 + 5w)
\]
So, the factored form of \( 9 - 25w^{2} \) is:
\[
(3 - 5w)(3 + 5w)
\]
**Final Answer:**
\[
(3 - 5w)(3 + 5w)
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Mind Expander
Did you know that the expression \( 9 - 25w^2 \) is a classic example of a difference of squares? This is a nifty little algebraic identity where \( a^2 - b^2 = (a - b)(a + b) \). Here, you can see that 9 is \( 3^2 \) and \( 25w^2 \) is \( (5w)^2 \). So, we can rewrite it as \( (3 - 5w)(3 + 5w) \)! When you factor it like a superhero in the math realm, you get not only a solution but also a deeper understanding of how algebra operates. So, whenever you encounter a difference of squares, whip out that identity and tackle it with confidence! Now you can apply this practice to various equations that pop up in algebra, making it a powerful tool in your math toolbox!
