erweitern (1+x+x^2)^8

Lösung

erweitern

(1 + x + x^{2})^{8}

x^{16} + 8 x^{15} + 36 x^{14} + 112 x^{13} + 266 x^{12} + 504 x^{11} + 784 x^{10} + 1016 x^{9} + 1107 x^{8} + 1016 x^{7} + 784 x^{6} + 504 x^{5} + 266 x^{4} + 112 x^{3} + 36 x^{2} + 8 x + 1

Schritte zur Lösung

(1 + x + x^{2})^{8}

(1 + x + x^{2})^{8} = (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}) (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) (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}) (1 + x + x^{2}) : x^{16} + 8 x^{15} + 36 x^{14} + 112 x^{13} + 266 x^{12} + 504 x^{11} + 784 x^{10} + 1016 x^{9} + 1107 x^{8} + 1016 x^{7} + 784 x^{6} + 504 x^{5} + 266 x^{4} + 112 x^{3} + 36 x^{2} + 8 x + 1

= x^{16} + 8 x^{15} + 36 x^{14} + 112 x^{13} + 266 x^{12} + 504 x^{11} + 784 x^{10} + 1016 x^{9} + 1107 x^{8} + 1016 x^{7} + 784 x^{6} + 504 x^{5} + 266 x^{4} + 112 x^{3} + 36 x^{2} + 8 x + 1

s im pl i f y 3 (3 - 2)

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

\frac{d ^{2}}{d k ^{2}} ((y (k, x)) (e^{4 x} - k x))

e x p an d x^{2} (1 - 4 e^{x})

e x p an d \frac{x ^{4}}{( x ^{2} - x + 1 ) ( x ^{2} + 2 ) ^{2}}