erweitern (x^2-2x+9)^7

Lösung

erweitern

(x^{2} - 2 x + 9)^{7}

x^{14} - 14 x^{13} + 147 x^{12} - 1036 x^{11} + 6041 x^{10} - 27762 x^{9} + 109123 x^{8} - 352424 x^{7} + 982107 x^{6} - 2248722 x^{5} + 4403889 x^{4} - 6797196 x^{3} + 8680203 x^{2} - 7440174 x + 4782969

Schritte zur Lösung

(x^{2} - 2 x + 9)^{7}

(x^{2} - 2 x + 9)^{7} = (x^{2} - 2 x + 9) (x^{2} - 2 x + 9) (x^{2} - 2 x + 9) (x^{2} - 2 x + 9) (x^{2} - 2 x + 9) (x^{2} - 2 x + 9) (x^{2} - 2 x + 9)

= (x^{2} - 2 x + 9) (x^{2} - 2 x + 9) (x^{2} - 2 x + 9) (x^{2} - 2 x + 9) (x^{2} - 2 x + 9) (x^{2} - 2 x + 9) (x^{2} - 2 x + 9)

Multipliziere aus

(x^{2} - 2 x + 9) (x^{2} - 2 x + 9) (x^{2} - 2 x + 9) (x^{2} - 2 x + 9) (x^{2} - 2 x + 9) (x^{2} - 2 x + 9) (x^{2} - 2 x + 9) : x^{14} - 14 x^{13} + 147 x^{12} - 1036 x^{11} + 6041 x^{10} - 27762 x^{9} + 109123 x^{8} - 352424 x^{7} + 982107 x^{6} - 2248722 x^{5} + 4403889 x^{4} - 6797196 x^{3} + 8680203 x^{2} - 7440174 x + 4782969

= x^{14} - 14 x^{13} + 147 x^{12} - 1036 x^{11} + 6041 x^{10} - 27762 x^{9} + 109123 x^{8} - 352424 x^{7} + 982107 x^{6} - 2248722 x^{5} + 4403889 x^{4} - 6797196 x^{3} + 8680203 x^{2} - 7440174 x + 4782969

s im pl i f y (v + v^{2} + 1)^{2}

s im pl i f y (m + 1)^{2}

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

e x p an d (x - 7) l e f t (x - 6)

s im pl i f y (3 i + 5) 3 e^{i t}