erweitern (x+x^3+x^5)^7

Lösung

erweitern

(x + x^{3} + x^{5})^{7}

x^{35} + 7 x^{33} + 28 x^{31} + 77 x^{29} + 161 x^{27} + 266 x^{25} + 357 x^{23} + 393 x^{21} + 357 x^{19} + 266 x^{17} + 161 x^{15} + 77 x^{13} + 28 x^{11} + 7 x^{9} + x^{7}

Schritte zur Lösung

(x + x^{3} + x^{5})^{7}

(x + x^{3} + x^{5})^{7} = (x + x^{3} + x^{5}) (x + x^{3} + x^{5}) (x + x^{3} + x^{5}) (x + x^{3} + x^{5}) (x + x^{3} + x^{5}) (x + x^{3} + x^{5}) (x + x^{3} + x^{5})

= (x^{5} + x^{3} + x) (x^{5} + x^{3} + x) (x^{5} + x^{3} + x) (x^{5} + x^{3} + x) (x^{5} + x^{3} + x) (x^{5} + x^{3} + x) (x^{5} + x^{3} + x)

Multipliziere aus

(x + x^{3} + x^{5}) (x + x^{3} + x^{5}) (x + x^{3} + x^{5}) (x + x^{3} + x^{5}) (x + x^{3} + x^{5}) (x + x^{3} + x^{5}) (x + x^{3} + x^{5}) : x^{35} + 7 x^{33} + 28 x^{31} + 77 x^{29} + 161 x^{27} + 266 x^{25} + 357 x^{23} + 393 x^{21} + 357 x^{19} + 266 x^{17} + 161 x^{15} + 77 x^{13} + 28 x^{11} + 7 x^{9} + x^{7}

= x^{35} + 7 x^{33} + 28 x^{31} + 77 x^{29} + 161 x^{27} + 266 x^{25} + 357 x^{23} + 393 x^{21} + 357 x^{19} + 266 x^{17} + 161 x^{15} + 77 x^{13} + 28 x^{11} + 7 x^{9} + x^{7}

e x p an d 3 e^{x} (e^{x} + 1)

e x p an d \frac{- 2 x - 6}{( x + 1 ) ( x - 1 )}

e x p an d 2 e^{- x} x - e^{- x} (x^{2} + 1)

e x p an d \frac{x ^{3} + x ^{2} + 1}{x ( x - 1 ) ^{2} ( x ^{2} + 5 ) ( x ^{2} + x + 1 )}

e x p an d \frac{1 - e ^{- s}}{s ( 1 + e ^{- s} )}