Questions: (3x^2/2 + 2/3 x + 1/2) · (1/2 x^2 + 2 x - 1)

(3x^2/2 + 2/3 x + 1/2) · (1/2 x^2 + 2 x - 1)
Transcript text: $\left(\frac{3 x^{2}}{2}+\frac{2}{3} x+\frac{1}{2}\right) \cdot\left(\frac{1}{2} x^{2}+2 x-1\right)$
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Solution

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To solve the given expression, we need to perform polynomial multiplication. This involves distributing each term in the first polynomial by each term in the second polynomial and then combining like terms.

Paso 1: Definición de los polinomios

Definimos los polinomios que vamos a multiplicar: \[ P_1 = \frac{3}{2}x^2 + \frac{2}{3}x + \frac{1}{2} \] \[ P_2 = \frac{1}{2}x^2 + 2x - 1 \]

Paso 2: Multiplicación de los polinomios

Multiplicamos \(P_1\) y \(P_2\): \[ P_1 \cdot P_2 = \left(\frac{3}{2}x^2 + \frac{2}{3}x + \frac{1}{2}\right) \cdot \left(\frac{1}{2}x^2 + 2x - 1\right) \]

Paso 3: Expansión y combinación de términos

Al expandir y combinar los términos, obtenemos: \[ P_1 \cdot P_2 = 0.75x^4 + 3.3333x^3 + 0.0833x^2 + 0.3333x - 0.5 \]

Respuesta Final

La expresión resultante de la multiplicación de los polinomios es: \[ \boxed{0.75x^4 + 3.3333x^3 + 0.0833x^2 + 0.3333x - 0.5} \]

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