erweitern (x^3+3x^2-4x+3)^5

Lösung

erweitern

(x^{3} + 3 x^{2} - 4 x + 3)^{5}

x^{15} + 15 x^{14} + 70 x^{13} + 45 x^{12} - 335 x^{11} + 93 x^{10} + 1610 x^{9} - 2535 x^{8} - 970 x^{7} + 9180 x^{6} - 16324 x^{5} + 17070 x^{4} - 11835 x^{3} + 5535 x^{2} - 1620 x + 243

Schritte zur Lösung

(x^{3} + 3 x^{2} - 4 x + 3)^{5}

(x^{3} + 3 x^{2} - 4 x + 3)^{5} = (x^{3} + 3 x^{2} - 4 x + 3) (x^{3} + 3 x^{2} - 4 x + 3) (x^{3} + 3 x^{2} - 4 x + 3) (x^{3} + 3 x^{2} - 4 x + 3) (x^{3} + 3 x^{2} - 4 x + 3)

= (x^{3} + 3 x^{2} - 4 x + 3) (x^{3} + 3 x^{2} - 4 x + 3) (x^{3} + 3 x^{2} - 4 x + 3) (x^{3} + 3 x^{2} - 4 x + 3) (x^{3} + 3 x^{2} - 4 x + 3)

Multipliziere aus

(x^{3} + 3 x^{2} - 4 x + 3) (x^{3} + 3 x^{2} - 4 x + 3) (x^{3} + 3 x^{2} - 4 x + 3) (x^{3} + 3 x^{2} - 4 x + 3) (x^{3} + 3 x^{2} - 4 x + 3) : x^{15} + 15 x^{14} + 70 x^{13} + 45 x^{12} - 335 x^{11} + 93 x^{10} + 1610 x^{9} - 2535 x^{8} - 970 x^{7} + 9180 x^{6} - 16324 x^{5} + 17070 x^{4} - 11835 x^{3} + 5535 x^{2} - 1620 x + 243

= x^{15} + 15 x^{14} + 70 x^{13} + 45 x^{12} - 335 x^{11} + 93 x^{10} + 1610 x^{9} - 2535 x^{8} - 970 x^{7} + 9180 x^{6} - 16324 x^{5} + 17070 x^{4} - 11835 x^{3} + 5535 x^{2} - 1620 x + 243

s im pl i f y x (x - 5) (x + 5 + 22) (x + 5 - 22)

s im pl i f y (x + x + 4)^{2}

e x p an d \frac{( s ( s + 5 ) ( s + 6 ) ( s ^{2} + 2 s + 2 ) )}{s + 3}

s im pl i f y (\frac{226}{2} + 2) (\frac{226}{2} - 2) (11)

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