erweitern (3x^2+x+2)^9

Lösung

erweitern

(3 x^{2} + x + 2)^{9}

19683 x^{18} + 59049 x^{17} + 196830 x^{16} + 376164 x^{15} + 712962 x^{14} + 989982 x^{13} + 1329048 x^{12} + 1415556 x^{11} + 1447011 x^{10} + 1207009 x^{9} + 964674 x^{8} + 629136 x^{7} + 393792 x^{6} + 195552 x^{5} + 93888 x^{4} + 33024 x^{3} + 11520 x^{2} + 2304 x + 512

Schritte zur Lösung

(3 x^{2} + x + 2)^{9}

(3 x^{2} + x + 2)^{9} = (3 x^{2} + x + 2) (3 x^{2} + x + 2) (3 x^{2} + x + 2) (3 x^{2} + x + 2) (3 x^{2} + x + 2) (3 x^{2} + x + 2) (3 x^{2} + x + 2) (3 x^{2} + x + 2) (3 x^{2} + x + 2)

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

Multipliziere aus

(3 x^{2} + x + 2) (3 x^{2} + x + 2) (3 x^{2} + x + 2) (3 x^{2} + x + 2) (3 x^{2} + x + 2) (3 x^{2} + x + 2) (3 x^{2} + x + 2) (3 x^{2} + x + 2) (3 x^{2} + x + 2) : 19683 x^{18} + 59049 x^{17} + 196830 x^{16} + 376164 x^{15} + 712962 x^{14} + 989982 x^{13} + 1329048 x^{12} + 1415556 x^{11} + 1447011 x^{10} + 1207009 x^{9} + 964674 x^{8} + 629136 x^{7} + 393792 x^{6} + 195552 x^{5} + 93888 x^{4} + 33024 x^{3} + 11520 x^{2} + 2304 x + 512

= 19683 x^{18} + 59049 x^{17} + 196830 x^{16} + 376164 x^{15} + 712962 x^{14} + 989982 x^{13} + 1329048 x^{12} + 1415556 x^{11} + 1447011 x^{10} + 1207009 x^{9} + 964674 x^{8} + 629136 x^{7} + 393792 x^{6} + 195552 x^{5} + 93888 x^{4} + 33024 x^{3} + 11520 x^{2} + 2304 x + 512

e x p an d P (k) \Rightarrow P (k + 1)

e x p an d \frac{( 3 x + 2 ) ^{2}}{x ^{4}}

e x p an d 4 [k (k + 1) (k - 1)]

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

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