erweitern 1/2 ((a^2-1)/2+1/2 (e^{-2a}-1/(e^2)))

Lösung

erweitern

\frac{1}{2} (\frac{a ^{2} - 1}{2} + \frac{1}{2} (e^{- 2 a} - \frac{1}{e ^{2}}))

\frac{1}{4} e^{- 2 a} - \frac{1}{4} - \frac{1}{4 e ^{2}} + \frac{a ^{2}}{4}

Schritte zur Lösung

\frac{1}{2} (\frac{a ^{2} - 1}{2} + \frac{1}{2} (e^{- 2 a} - \frac{1}{e ^{2}}))

Wende das Distributivgesetz an:

a (b + c) = ab + a c

a = \frac{1}{2}, b = \frac{a ^{2} - 1}{2}, c = \frac{1}{2} (e^{- 2 a} - \frac{1}{e ^{2}})

= \frac{1}{2} \cdot \frac{a ^{2} - 1}{2} + \frac{1}{2} \cdot \frac{1}{2} (e^{- 2 a} - \frac{1}{e ^{2}})

Vereinfache

\frac{1}{2} \cdot \frac{a ^{2} - 1}{2} + \frac{1}{2} \cdot \frac{1}{2} (e^{- 2 a} - \frac{1}{e ^{2}}) : \frac{1}{4} e^{- 2 a} - \frac{1}{4} - \frac{1}{4 e ^{2}} + \frac{a ^{2}}{4}

= \frac{1}{4} e^{- 2 a} - \frac{1}{4} - \frac{1}{4 e ^{2}} + \frac{a ^{2}}{4}

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e x p an d (8 e^{t} cos (t) - 8 e^{t} sin (t))^{2}

e x p an d (- 4, - 2) y (4, - 4)

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e x p an d (m^{4} - 0, t) (m^{4} + 0, 7)