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Factor the expression, then simplify if possible. 25x² - 4y²

Factor the expression, then simplify if possible. 25x² - 4y²

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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**Problem:** Factor the expression, then simplify if possible. \[ 25x^2 - 4y^2 \] **Answer Choices:** A. \((5x + 2y)(5x - 2y)\) B. \((5x - 2y)(5x - 2y)\) C. \((5x + 2y)(5x + 2y)\) D. \((5x + 2y)(5 - 2)\) **Explanation:** The expression \(25x^2 - 4y^2\) can be factored using the difference of squares formula: \((a^2 - b^2) = (a + b)(a - b)\). In this case: - \(a^2 = 25x^2\), so \(a = 5x\). - \(b^2 = 4y^2\), so \(b = 2y\). Applying the formula: \[ 25x^2 - 4y^2 = (5x + 2y)(5x - 2y) \] Thus, the correct answer is **A. \((5x + 2y)(5x - 2y)\)**.
Transcribed Image Text:**Problem:** Factor the expression, then simplify if possible. \[ 25x^2 - 4y^2 \] **Answer Choices:** A. \((5x + 2y)(5x - 2y)\) B. \((5x - 2y)(5x - 2y)\) C. \((5x + 2y)(5x + 2y)\) D. \((5x + 2y)(5 - 2)\) **Explanation:** The expression \(25x^2 - 4y^2\) can be factored using the difference of squares formula: \((a^2 - b^2) = (a + b)(a - b)\). In this case: - \(a^2 = 25x^2\), so \(a = 5x\). - \(b^2 = 4y^2\), so \(b = 2y\). Applying the formula: \[ 25x^2 - 4y^2 = (5x + 2y)(5x - 2y) \] Thus, the correct answer is **A. \((5x + 2y)(5x - 2y)\)**.
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