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\( \left.5 x^{2}-5 x+3\right) \) 16) \( (2 a-3 b)^{3}(a-b) \)

Ask by Chan John. in Venezuela
Mar 16,2025

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**Expresión \(5x^2 - 5x + 3\):** - No se puede factorizar ya que el discriminante es negativo. **Expresión \((2a - 3b)^3 (a - b)\):** - Desarrollada: \(8a^4 - 44a^3b + 90a^2b^2 - 81ab^3 + 27b^4\).

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Beyond the Answer

Did you know that the expression \( 5x^2 - 5x + 3 \) resembles a quadratic equation? Quadratics have been around since ancient civilizations. The Babylonians were among the first to solve quadratic equations over 4,000 years ago, using geometric methods that laid the groundwork for algebra as we know it today! When you encounter expressions like \( (2a - 3b)^3(a - b) \), consider how to expand them thoughtfully. A common mistake here is overlooking the distributive property. Make sure to apply it carefully, ensuring that both terms are multiplied correctly. A helpful tip is to tackle one part at a time—expand \( (2a - 3b)^3 \) separately before integrating it with \( (a - b) \). Happy calculating!

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