erweitern (1-x-x^2)^7

Lösung

erweitern

(1 - x - x^{2})^{7}

- x^{14} - 7 x^{13} - 14 x^{12} + 7 x^{11} + 49 x^{10} + 14 x^{9} - 77 x^{8} - 29 x^{7} + 77 x^{6} + 14 x^{5} - 49 x^{4} + 7 x^{3} + 14 x^{2} - 7 x + 1

Schritte zur Lösung

(1 - x - x^{2})^{7}

(1 - x - x^{2})^{7} = (1 - x - x^{2}) (1 - x - x^{2}) (1 - x - x^{2}) (1 - x - x^{2}) (1 - x - x^{2}) (1 - x - x^{2}) (1 - x - x^{2})

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

Multipliziere aus

(1 - x - x^{2}) (1 - x - x^{2}) (1 - x - x^{2}) (1 - x - x^{2}) (1 - x - x^{2}) (1 - x - x^{2}) (1 - x - x^{2}) : - x^{14} - 7 x^{13} - 14 x^{12} + 7 x^{11} + 49 x^{10} + 14 x^{9} - 77 x^{8} - 29 x^{7} + 77 x^{6} + 14 x^{5} - 49 x^{4} + 7 x^{3} + 14 x^{2} - 7 x + 1

= - x^{14} - 7 x^{13} - 14 x^{12} + 7 x^{11} + 49 x^{10} + 14 x^{9} - 77 x^{8} - 29 x^{7} + 77 x^{6} + 14 x^{5} - 49 x^{4} + 7 x^{3} + 14 x^{2} - 7 x + 1

e x p an d \frac{( x - 2 ) x}{( x + 3 ) \cdot 2}

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

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

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

e x p an d (2 x + 3) y^{'} (x)