erweitern (c^2-3bd+12ae)^3

Lösung

erweitern

(c^{2} - 3 b d + 12 a e)^{3}

c^{6} - 9 c^{4} b d + 36 e c^{4} a + 27 c^{2} b^{2} d^{2} + 432 e^{2} c^{2} a^{2} - 216 e c^{2} b d a - 27 b^{3} d^{3} + 1728 e^{3} a^{3} - 1296 e^{2} b d a^{2} + 324 e b^{2} d^{2} a

Schritte zur Lösung

(c^{2} - 3 b d + 12 a e)^{3}

= (c^{2} - 3 b d + 12 e a)^{3}

(c^{2} - 3 b d + 12 a e)^{3} = (c^{2} - 3 b d + 12 a e) (c^{2} - 3 b d + 12 a e) (c^{2} - 3 b d + 12 a e)

= (c^{2} + 12 e a - 3 b d) (c^{2} + 12 e a - 3 b d) (c^{2} + 12 e a - 3 b d)

Multipliziere aus

(c^{2} - 3 b d + 12 a e) (c^{2} - 3 b d + 12 a e) (c^{2} - 3 b d + 12 a e) : c^{6} - 9 c^{4} b d + 36 e c^{4} a + 27 c^{2} b^{2} d^{2} + 432 e^{2} c^{2} a^{2} - 216 e c^{2} b d a - 27 b^{3} d^{3} + 1728 e^{3} a^{3} - 1296 e^{2} b d a^{2} + 324 e b^{2} d^{2} a

= c^{6} - 9 c^{4} b d + 36 e c^{4} a + 27 c^{2} b^{2} d^{2} + 432 e^{2} c^{2} a^{2} - 216 e c^{2} b d a - 27 b^{3} d^{3} + 1728 e^{3} a^{3} - 1296 e^{2} b d a^{2} + 324 e b^{2} d^{2} a

e x p an d (x y cosh (x) + y sinh (x)) d x

e x p an d \frac{x ^{2} - 52 x + 33}{( 1 - x ) ( 2 x - 1 ) ( x - 5 )}

e x p an d \frac{2 r ^{2} + 2 a ^{2}}{( r + a ) ^{2} ( r - a ) ^{2}}

s im pl i f y e^{π (b - in)} - e^{- π (b - in)}

e x p an d \frac{( - 1 ) ^{\frac{1}{π}} ( e ^{4 π} - 1 )}{4 π e ^{2 π}}