Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
Related questions
Question
![**Topic: Difference of Squares with GCF**
Given Expression:
\[ 25x^2 - 100 \]
The expression can be identified as a difference of squares. It can be rewritten using the formula for difference of squares:
\[ a^2 - b^2 = (a + b)(a - b) \]
**Steps to Solve:**
1. **Identify the Common Factor (GCF):**
First, factor out the greatest common factor (GCF) of the expression.
- The GCF of \(25x^2\) and \(100\) is \(25\).
2. **Factor Out the GCF:**
- \( 25x^2 - 100 = 25(x^2 - 4) \)
3. **Difference of Squares:**
- The expression \(x^2 - 4\) is a difference of squares:
- \( x^2 - 4 = (x + 2)(x - 2) \)
4. **Final Factored Form:**
- Combining all parts:
- \( 25x^2 - 100 = 25(x + 2)(x - 2) \)
**Conclusion:**
The expression \(25x^2 - 100\) factors into \(25(x + 2)(x - 2)\), utilizing both the greatest common factor and the difference of squares method.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc37dbff0-e053-476c-a940-a199db5d9106%2F7137eb60-d29a-4d08-8404-af116a2ae21e%2Fn14o9o_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Topic: Difference of Squares with GCF**
Given Expression:
\[ 25x^2 - 100 \]
The expression can be identified as a difference of squares. It can be rewritten using the formula for difference of squares:
\[ a^2 - b^2 = (a + b)(a - b) \]
**Steps to Solve:**
1. **Identify the Common Factor (GCF):**
First, factor out the greatest common factor (GCF) of the expression.
- The GCF of \(25x^2\) and \(100\) is \(25\).
2. **Factor Out the GCF:**
- \( 25x^2 - 100 = 25(x^2 - 4) \)
3. **Difference of Squares:**
- The expression \(x^2 - 4\) is a difference of squares:
- \( x^2 - 4 = (x + 2)(x - 2) \)
4. **Final Factored Form:**
- Combining all parts:
- \( 25x^2 - 100 = 25(x + 2)(x - 2) \)
**Conclusion:**
The expression \(25x^2 - 100\) factors into \(25(x + 2)(x - 2)\), utilizing both the greatest common factor and the difference of squares method.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 3 images
Recommended textbooks for you
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press
College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education