erweitern (1-3x+x^2)^8

Lösung

erweitern

(1 - 3 x + x^{2})^{8}

x^{16} - 24 x^{15} + 260 x^{14} - 1680 x^{13} + 7210 x^{12} - 21672 x^{11} + 46928 x^{10} - 74280 x^{9} + 86515 x^{8} - 74280 x^{7} + 46928 x^{6} - 21672 x^{5} + 7210 x^{4} - 1680 x^{3} + 260 x^{2} - 24 x + 1

Schritte zur Lösung

(1 - 3 x + x^{2})^{8}

(1 - 3 x + x^{2})^{8} = (1 - 3 x + x^{2}) (1 - 3 x + x^{2}) (1 - 3 x + x^{2}) (1 - 3 x + x^{2}) (1 - 3 x + x^{2}) (1 - 3 x + x^{2}) (1 - 3 x + x^{2}) (1 - 3 x + x^{2})

= (x^{2} - 3 x + 1) (x^{2} - 3 x + 1) (x^{2} - 3 x + 1) (x^{2} - 3 x + 1) (x^{2} - 3 x + 1) (x^{2} - 3 x + 1) (x^{2} - 3 x + 1) (x^{2} - 3 x + 1)

Multipliziere aus

(1 - 3 x + x^{2}) (1 - 3 x + x^{2}) (1 - 3 x + x^{2}) (1 - 3 x + x^{2}) (1 - 3 x + x^{2}) (1 - 3 x + x^{2}) (1 - 3 x + x^{2}) (1 - 3 x + x^{2}) : x^{16} - 24 x^{15} + 260 x^{14} - 1680 x^{13} + 7210 x^{12} - 21672 x^{11} + 46928 x^{10} - 74280 x^{9} + 86515 x^{8} - 74280 x^{7} + 46928 x^{6} - 21672 x^{5} + 7210 x^{4} - 1680 x^{3} + 260 x^{2} - 24 x + 1

= x^{16} - 24 x^{15} + 260 x^{14} - 1680 x^{13} + 7210 x^{12} - 21672 x^{11} + 46928 x^{10} - 74280 x^{9} + 86515 x^{8} - 74280 x^{7} + 46928 x^{6} - 21672 x^{5} + 7210 x^{4} - 1680 x^{3} + 260 x^{2} - 24 x + 1

\frac{d}{d q} ((C) (7 + 2 q - 3 q^{2}))

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

e x p an d - \frac{5 ( y - 1 )}{13 ( y + 1 )}

e x p an d f (f (f (- 2.8) + 3, 5) - 1)

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