erweitern (x^3-2x+3)^7

Lösung

erweitern

(x^{3} - 2 x + 3)^{7}

x^{21} - 14 x^{19} + 21 x^{18} + 84 x^{17} - 252 x^{16} - 91 x^{15} + 1260 x^{14} - 1330 x^{13} - 2415 x^{12} + 6888 x^{11} - 2520 x^{10} - 11837 x^{9} + 18648 x^{8} - 2018 x^{7} - 23793 x^{6} + 27972 x^{5} - 5292 x^{4} - 17577 x^{3} + 20412 x^{2} - 10206 x + 2187

Schritte zur Lösung

(x^{3} - 2 x + 3)^{7}

(x^{3} - 2 x + 3)^{7} = (x^{3} - 2 x + 3) (x^{3} - 2 x + 3) (x^{3} - 2 x + 3) (x^{3} - 2 x + 3) (x^{3} - 2 x + 3) (x^{3} - 2 x + 3) (x^{3} - 2 x + 3)

= (x^{3} - 2 x + 3) (x^{3} - 2 x + 3) (x^{3} - 2 x + 3) (x^{3} - 2 x + 3) (x^{3} - 2 x + 3) (x^{3} - 2 x + 3) (x^{3} - 2 x + 3)

Multipliziere aus

(x^{3} - 2 x + 3) (x^{3} - 2 x + 3) (x^{3} - 2 x + 3) (x^{3} - 2 x + 3) (x^{3} - 2 x + 3) (x^{3} - 2 x + 3) (x^{3} - 2 x + 3) : x^{21} - 14 x^{19} + 21 x^{18} + 84 x^{17} - 252 x^{16} - 91 x^{15} + 1260 x^{14} - 1330 x^{13} - 2415 x^{12} + 6888 x^{11} - 2520 x^{10} - 11837 x^{9} + 18648 x^{8} - 2018 x^{7} - 23793 x^{6} + 27972 x^{5} - 5292 x^{4} - 17577 x^{3} + 20412 x^{2} - 10206 x + 2187

= x^{21} - 14 x^{19} + 21 x^{18} + 84 x^{17} - 252 x^{16} - 91 x^{15} + 1260 x^{14} - 1330 x^{13} - 2415 x^{12} + 6888 x^{11} - 2520 x^{10} - 11837 x^{9} + 18648 x^{8} - 2018 x^{7} - 23793 x^{6} + 27972 x^{5} - 5292 x^{4} - 17577 x^{3} + 20412 x^{2} - 10206 x + 2187

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

s im pl i f y (x^{2} - 4) (x^{2} - \frac{2}{3})

s im pl i f y (x - 2) (x + 5)

e x p an d π (82 - \frac{56 2}{15})

e x p an d (1 + 2)^{8}