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,...
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![**Lesson: Difference of Squares**
**Example 1: \(x^2 - 4\)**
This is an example of the "difference of squares." In algebra, a difference of squares is a specific type of binomial that can be factored into two conjugate binomials. The general form is:
\[ a^2 - b^2 = (a + b)(a - b) \]
**Explanation:**
- In the expression \(x^2 - 4\), \(x^2\) and \(4\) are both perfect squares.
- Here, \(x^2\) is the square of \(x\), and \(4\) is the square of \(2\).
- Applying the difference of squares formula, we get:
\[ x^2 - 4 = (x + 2)(x - 2) \]
This factorization is useful for simplifying expressions and solving equations where a difference of squares is present.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc37dbff0-e053-476c-a940-a199db5d9106%2F483aaddc-426a-43a5-bc80-2478901ad647%2F2ylhwsc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Lesson: Difference of Squares**
**Example 1: \(x^2 - 4\)**
This is an example of the "difference of squares." In algebra, a difference of squares is a specific type of binomial that can be factored into two conjugate binomials. The general form is:
\[ a^2 - b^2 = (a + b)(a - b) \]
**Explanation:**
- In the expression \(x^2 - 4\), \(x^2\) and \(4\) are both perfect squares.
- Here, \(x^2\) is the square of \(x\), and \(4\) is the square of \(2\).
- Applying the difference of squares formula, we get:
\[ x^2 - 4 = (x + 2)(x - 2) \]
This factorization is useful for simplifying expressions and solving equations where a difference of squares is present.
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