erweitern (x^2-x+4)^8

Lösung

erweitern

(x^{2} - x + 4)^{8}

x^{16} - 8 x^{15} + 60 x^{14} - 280 x^{13} + 1190 x^{12} - 3864 x^{11} + 11452 x^{10} - 27560 x^{9} + 60705 x^{8} - 110240 x^{7} + 183232 x^{6} - 247296 x^{5} + 304640 x^{4} - 286720 x^{3} + 245760 x^{2} - 131072 x + 65536

Schritte zur Lösung

(x^{2} - x + 4)^{8}

(x^{2} - x + 4)^{8} = (x^{2} - x + 4) (x^{2} - x + 4) (x^{2} - x + 4) (x^{2} - x + 4) (x^{2} - x + 4) (x^{2} - x + 4) (x^{2} - x + 4) (x^{2} - x + 4)

= (x^{2} - x + 4) (x^{2} - x + 4) (x^{2} - x + 4) (x^{2} - x + 4) (x^{2} - x + 4) (x^{2} - x + 4) (x^{2} - x + 4) (x^{2} - x + 4)

Multipliziere aus

(x^{2} - x + 4) (x^{2} - x + 4) (x^{2} - x + 4) (x^{2} - x + 4) (x^{2} - x + 4) (x^{2} - x + 4) (x^{2} - x + 4) (x^{2} - x + 4) : x^{16} - 8 x^{15} + 60 x^{14} - 280 x^{13} + 1190 x^{12} - 3864 x^{11} + 11452 x^{10} - 27560 x^{9} + 60705 x^{8} - 110240 x^{7} + 183232 x^{6} - 247296 x^{5} + 304640 x^{4} - 286720 x^{3} + 245760 x^{2} - 131072 x + 65536

= x^{16} - 8 x^{15} + 60 x^{14} - 280 x^{13} + 1190 x^{12} - 3864 x^{11} + 11452 x^{10} - 27560 x^{9} + 60705 x^{8} - 110240 x^{7} + 183232 x^{6} - 247296 x^{5} + 304640 x^{4} - 286720 x^{3} + 245760 x^{2} - 131072 x + 65536

e x p an d \frac{( x - 1 ) ( x + 1 )}{( x + 5 ) ( x - 5 )}

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

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

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

\frac{d ^{2}}{d t ^{2}} ((v) (a v (t) - b v (t) ln (v)))