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(c) factarse, \( 4 x^{2}-5^{2} x+\frac{9}{25} \)

Ask by Moreno Mcfarlane. in Nigeria
Feb 21,2025

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The factored form is \(\frac{1}{25}(100x^{2}-625x+9)\).

Solución

Factor the expression \( 4x^2-5^2x+\frac{9}{25} \). Factor the expression by following steps: - step0: Factor: \(4x^{2}-5^{2}x+\frac{9}{25}\) - step1: Factor the expression: \(\frac{1}{25}\left(100x^{2}-625x+9\right)\) The factored form of the expression \(4x^2-5^2x+\frac{9}{25}\) is \(\frac{1}{25}(100x^{2}-625x+9)\).

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Para factorizar la expresión cuadrática \( 4x^{2} - 5^{2}x + \frac{9}{25} \), primero observamos que se puede escribir como un trinomio de la forma \( ax^2 + bx + c \). Aquí, podemos aplicar la fórmula de factorización o intentar agrupar. Observando que \( 4x^{2} \) es un cuadrado perfecto, y que también \( \left(\frac{3}{5}\right)^2 = \frac{9}{25} \), reconocemos que podemos reorganizar y agrupar adecuadamente para obtener: \[ 4x^{2} - 5x + \frac{9}{25} = (2x - \frac{3}{5})^2 \] Ahora hemos factorizado la expresión, ¡y todo gracias a los cuadrados perfectos! Para asegurarte que la factorización es correcta, puedes realizar la expansión. Al hacerlo, notarás que los términos coinciden, así que el resultado final es: \[ (2x - \frac{3}{5})^2 \] ¡Y voilà! Hemos descompuesto la expresión de manera correcta.

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