erweitern (3x^3-4x-2)^6

Lösung

erweitern

(3 x^{3} - 4 x - 2)^{6}

729 x^{18} - 5832 x^{16} - 2916 x^{15} + 19440 x^{14} + 19440 x^{13} - 29700 x^{12} - 51840 x^{11} + 8640 x^{10} + 64800 x^{9} + 33408 x^{8} - 28800 x^{7} - 39824 x^{6} - 10752 x^{5} + 9600 x^{4} + 9664 x^{3} + 3840 x^{2} + 768 x + 64

Schritte zur Lösung

(3 x^{3} - 4 x - 2)^{6}

(3 x^{3} - 4 x - 2)^{6} = (3 x^{3} - 4 x - 2) (3 x^{3} - 4 x - 2) (3 x^{3} - 4 x - 2) (3 x^{3} - 4 x - 2) (3 x^{3} - 4 x - 2) (3 x^{3} - 4 x - 2)

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

Multipliziere aus

(3 x^{3} - 4 x - 2) (3 x^{3} - 4 x - 2) (3 x^{3} - 4 x - 2) (3 x^{3} - 4 x - 2) (3 x^{3} - 4 x - 2) (3 x^{3} - 4 x - 2) : 729 x^{18} - 5832 x^{16} - 2916 x^{15} + 19440 x^{14} + 19440 x^{13} - 29700 x^{12} - 51840 x^{11} + 8640 x^{10} + 64800 x^{9} + 33408 x^{8} - 28800 x^{7} - 39824 x^{6} - 10752 x^{5} + 9600 x^{4} + 9664 x^{3} + 3840 x^{2} + 768 x + 64

= 729 x^{18} - 5832 x^{16} - 2916 x^{15} + 19440 x^{14} + 19440 x^{13} - 29700 x^{12} - 51840 x^{11} + 8640 x^{10} + 64800 x^{9} + 33408 x^{8} - 28800 x^{7} - 39824 x^{6} - 10752 x^{5} + 9600 x^{4} + 9664 x^{3} + 3840 x^{2} + 768 x + 64

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

e x p an d - \frac{1}{4} (1 - s) (1 - t) + (- \frac{1}{4}) (1 + s) (1 - t)

e x p an d \frac{15}{( x + 2 ) ^{2}}

s im pl i f y (x - a) \cdot (x - \frac{a + 2 b}{3}) \cdot (x - b)

e x p an d \frac{3}{4} (x - 4 = - \frac{1}{4} (x - 16))