erweitern x^{4/5}× (x-4)^2

Lösung

erweitern

x^{\frac{4}{5}} \cdot (x - 4)^{2}

x^{\frac{14}{5}} - 8 x^{\frac{9}{5}} + x^{\frac{4}{5}} \cdot 16

Schritte zur Lösung

x^{\frac{4}{5}} (x - 4)^{2}

Schreibe

(x - 4)^{2}

um:

x^{2} - 8 x + 16

= x^{\frac{4}{5}} (x^{2} - 8 x + 16)

Wende das Distributivgesetz an:

m (a + b + c) = ma + mb + m c

x^{\frac{4}{5}} (x^{2} - 8 x + 16) = x^{\frac{4}{5}} x^{2} + x^{\frac{4}{5}} (- 8 x) + x^{\frac{4}{5}} \cdot 16

= x^{\frac{4}{5}} x^{2} + x^{\frac{4}{5}} (- 8 x) + x^{\frac{4}{5}} \cdot 16

x^{\frac{4}{5}} x^{2} = x^{\frac{14}{5}}

x^{\frac{4}{5}} (- 8 x) = - 8 x^{\frac{9}{5}}

= x^{\frac{14}{5}} - 8 x^{\frac{9}{5}} + x^{\frac{4}{5}} \cdot 16

e x p an d \frac{e ^{- t} t ^{2} ( 14 + 2 t )}{9} + 15 - 10 t

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