erweitern (3/b+4e)^3

Lösung

erweitern

(\frac{3}{b} + 4 e)^{3}

\frac{27}{b ^{3}} + \frac{108 e}{b ^{2}} + \frac{144 e ^{2}}{b} + 64 e^{3}

Schritte zur Lösung

(\frac{3}{b} + 4 e)^{3}

Wende Formel für perfekte dritte Potenzen an:

(a + b)^{3} = a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3}

a = \frac{3}{b}, b = 4 e

= (\frac{3}{b})^{3} + 3 (\frac{3}{b})^{2} \cdot 4 e + 3 \cdot \frac{3}{b} (4 e)^{2} + (4 e)^{3}

Vereinfache

(\frac{3}{b})^{3} + 3 (\frac{3}{b})^{2} \cdot 4 e + 3 \cdot \frac{3}{b} (4 e)^{2} + (4 e)^{3} : \frac{27}{b ^{3}} + \frac{108 e}{b ^{2}} + \frac{144 e ^{2}}{b} + 64 e^{3}

= \frac{27}{b ^{3}} + \frac{108 e}{b ^{2}} + \frac{144 e ^{2}}{b} + 64 e^{3}

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