erweitern (12Je^{36Jβ}+6Je^{12Jβ})^2

Lösung

erweitern

(12 J e^{36 J β} + 6 J e^{12 J β})^{2}

144 e^{72 β J} J^{2} + 144 e^{48 β J} J^{2} + 36 e^{24 β J} J^{2}

Schritte zur Lösung

(12 J e^{36 J β} + 6 J e^{12 J β})^{2}

= (12 e^{36 β J} J + 6 e^{12 β J} J)^{2}

Wende Formel für perfekte quadratische Gleichungen an:

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

a = 12 J e^{36 J β}, b = 6 J e^{12 J β}

= (12 J e^{36 J β})^{2} + 2 \cdot 12 J e^{36 J β} \cdot 6 J e^{12 J β} + (6 J e^{12 J β})^{2}

Vereinfache

(12 J e^{36 J β})^{2} + 2 \cdot 12 J e^{36 J β} \cdot 6 J e^{12 J β} + (6 J e^{12 J β})^{2} : 144 e^{72 β J} J^{2} + 144 e^{48 β J} J^{2} + 36 e^{24 β J} J^{2}

= 144 e^{72 β J} J^{2} + 144 e^{48 β J} J^{2} + 36 e^{24 β J} J^{2}

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e x p an d (3 x - \frac{x ^{2}}{3})^{13}

s im pl i f y - i ((1 + i)^{n} - 1)

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e x p an d \frac{cos ( x )}{2 ( 1 + sin ( x ) )}