erweitern (1+x-x^2)^6

Lösung

erweitern

(1 + x - x^{2})^{6}

x^{12} - 6 x^{11} + 9 x^{10} + 10 x^{9} - 30 x^{8} - 6 x^{7} + 41 x^{6} + 6 x^{5} - 30 x^{4} - 10 x^{3} + 9 x^{2} + 6 x + 1

Schritte zur Lösung

(1 + x - x^{2})^{6}

(1 + x - x^{2})^{6} = (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)

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}) : x^{12} - 6 x^{11} + 9 x^{10} + 10 x^{9} - 30 x^{8} - 6 x^{7} + 41 x^{6} + 6 x^{5} - 30 x^{4} - 10 x^{3} + 9 x^{2} + 6 x + 1

= x^{12} - 6 x^{11} + 9 x^{10} + 10 x^{9} - 30 x^{8} - 6 x^{7} + 41 x^{6} + 6 x^{5} - 30 x^{4} - 10 x^{3} + 9 x^{2} + 6 x + 1

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

e x p an d π (2 x + 2 y)

e x p an d \frac{x ( y - x )}{y}

e x p an d \frac{x - 5 ( x + 4 + 3 )}{x + 13}

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