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

Lösung

erweitern

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

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

Schritte zur Lösung

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

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

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

Multipliziere aus

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

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

e x p an d (- 3 + 2) (3 + 5)

e x p an d e^{c o s (x)} (1 - cos (y))

e x p an d V (2, 5, - 2, 25)

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

s im pl i f y 4 (105 + \frac{- 4 2 - 50 5}{15})