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1. ²-4 Difference of squares

1. ²-4 Difference of squares

Algebra and Trigonometry (6th Edition)
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.
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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