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

Lösung

erweitern

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

- x^{14} + 14 x^{13} - 77 x^{12} + 196 x^{11} - 161 x^{10} - 238 x^{9} + 427 x^{8} + 184 x^{7} - 427 x^{6} - 238 x^{5} + 161 x^{4} + 196 x^{3} + 77 x^{2} + 14 x + 1

Schritte zur Lösung

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

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

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

Multipliziere aus

(1 + 2 x - x^{2}) (1 + 2 x - x^{2}) (1 + 2 x - x^{2}) (1 + 2 x - x^{2}) (1 + 2 x - x^{2}) (1 + 2 x - x^{2}) (1 + 2 x - x^{2}) : - x^{14} + 14 x^{13} - 77 x^{12} + 196 x^{11} - 161 x^{10} - 238 x^{9} + 427 x^{8} + 184 x^{7} - 427 x^{6} - 238 x^{5} + 161 x^{4} + 196 x^{3} + 77 x^{2} + 14 x + 1

= - x^{14} + 14 x^{13} - 77 x^{12} + 196 x^{11} - 161 x^{10} - 238 x^{9} + 427 x^{8} + 184 x^{7} - 427 x^{6} - 238 x^{5} + 161 x^{4} + 196 x^{3} + 77 x^{2} + 14 x + 1

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

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

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

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

s im pl i f y - (\frac{9}{14} lo g_{2} (\frac{9}{14}) + \frac{5}{14} lo g_{2} (\frac{5}{14}))