Espressioni con i monomi – Esercizio 6

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Esercizio. $(\bigstar\largewhitestar\largewhitestar)$

Semplificare la seguente espressione

$a^2\left(-\dfrac{1}{2}a\right) (-4ax^2)+\left(-\dfrac{2}{3}a^3x\right)\left(+\dfrac{3}{4}ax\right)$

Soluzione.

$\begin{aligned} a^2\left(-\dfrac{1}{2}a\right) (-4ax^2)+\left(-\dfrac{2}{3}a^3x\right)\left(+\dfrac{3}{4}ax\right) & = \left(-\dfrac{1}{2}a^3\right) \left(-4ax^2\right) - \dfrac{2}{3} \cdot \dfrac{3}{4} a^4x^2 = \\\\ & = 2a^4x^2-\dfrac{1}{2}a^4x^2 = \\\\ & = \left(2-\dfrac{1}{2}\right)a^4x^2 = \text{\fbox{$ \dfrac{3}{2}a^4x^2$}} \end{aligned}$