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Factor the difference of two squares. 25x² - 36 25x² - 36 =

Factor the difference of two squares. 25x² - 36 25x² - 36 =

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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Question
**Factoring the Difference of Two Squares** **Problem:** Factor the difference of two squares: \[ 25x^2 - 36 \] **Solution:** The expression \( 25x^2 - 36 \) is a classic example of the difference of two squares, which can be factored using the formula: \[ a^2 - b^2 = (a + b)(a - b) \] To apply this formula, we first identify \( a^2 \) and \( b^2 \): - \( 25x^2 = (5x)^2 \) - \( 36 = (6)^2 \) So, \( a = 5x \) and \( b = 6 \). Substitute these into the formula: \[ 25x^2 - 36 = (5x + 6)(5x - 6) \] Thus, the factored form of \( 25x^2 - 36 \) is: \[ (5x + 6)(5x - 6) \] **Note:** Make sure to verify the factorization by expanding the factors to ensure they simplify back to the original expression: \[ (5x + 6)(5x - 6) = 25x^2 - 30x + 30x - 36 = 25x^2 - 36 \]
Transcribed Image Text:**Factoring the Difference of Two Squares** **Problem:** Factor the difference of two squares: \[ 25x^2 - 36 \] **Solution:** The expression \( 25x^2 - 36 \) is a classic example of the difference of two squares, which can be factored using the formula: \[ a^2 - b^2 = (a + b)(a - b) \] To apply this formula, we first identify \( a^2 \) and \( b^2 \): - \( 25x^2 = (5x)^2 \) - \( 36 = (6)^2 \) So, \( a = 5x \) and \( b = 6 \). Substitute these into the formula: \[ 25x^2 - 36 = (5x + 6)(5x - 6) \] Thus, the factored form of \( 25x^2 - 36 \) is: \[ (5x + 6)(5x - 6) \] **Note:** Make sure to verify the factorization by expanding the factors to ensure they simplify back to the original expression: \[ (5x + 6)(5x - 6) = 25x^2 - 30x + 30x - 36 = 25x^2 - 36 \]
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