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E. EJERCICIO \#4: Factoriza cada uno de los binomios aplicando factor común. \[ \begin{array}{l}\text { A*). } 24 x^{3} y^{2}-75 h^{4} y^{5} \\ \text { B*). }^{*}-15 a^{2} b^{4}+40 a^{3} c^{2}\end{array} \]

Ask by Parry Simpson. in Colombia
Mar 12,2025

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\[ \textbf{A*) } 24x^3y^2 - 75h^4y^5 = 3y^2(8x^3 - 25h^4y^3) \] \[ \textbf{B*) } -15a^2b^4 + 40a^3c^2 = 5a^2(-3b^4 + 8ac^2) \]

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Para factorizar el primer binomio, \( 24x^3y^2 - 75h^4y^5 \), primero identificamos el factor común. El máximo común divisor (MCD) de los coeficientes 24 y 75 es 3. Observamos también que \(y^2\) es el factor común en ambos términos. Así que, al extraer \(3y^2\), tenemos: \[ 3y^2(8x^3 - 25h^4y^3) \]. En el segundo binomio, \(-15a^2b^4 + 40a^3c^2\), el MCD de los coeficientes \(-15\) y \(40\) es 5. Además, observamos que \(a^2\) es el factor común. Así que, al extraer \(-5a^2\), logramos: \[ -5a^2(3b^4 - 8a c^2) \]. ¡Listo! Estos binomios ya están factorizados exitosamente.

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