erweitern (3x^4+6x^2-2)^5

Lösung

erweitern

(3 x^{4} + 6 x^{2} - 2)^{5}

243 x^{20} + 2430 x^{18} + 8910 x^{16} + 12960 x^{14} + 1080 x^{12} - 11664 x^{10} - 720 x^{8} + 5760 x^{6} - 2640 x^{4} + 480 x^{2} - 32

Schritte zur Lösung

(3 x^{4} + 6 x^{2} - 2)^{5}

(3 x^{4} + 6 x^{2} - 2)^{5} = (3 x^{4} + 6 x^{2} - 2) (3 x^{4} + 6 x^{2} - 2) (3 x^{4} + 6 x^{2} - 2) (3 x^{4} + 6 x^{2} - 2) (3 x^{4} + 6 x^{2} - 2)

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

Multipliziere aus

(3 x^{4} + 6 x^{2} - 2) (3 x^{4} + 6 x^{2} - 2) (3 x^{4} + 6 x^{2} - 2) (3 x^{4} + 6 x^{2} - 2) (3 x^{4} + 6 x^{2} - 2) : 243 x^{20} + 2430 x^{18} + 8910 x^{16} + 12960 x^{14} + 1080 x^{12} - 11664 x^{10} - 720 x^{8} + 5760 x^{6} - 2640 x^{4} + 480 x^{2} - 32

= 243 x^{20} + 2430 x^{18} + 8910 x^{16} + 12960 x^{14} + 1080 x^{12} - 11664 x^{10} - 720 x^{8} + 5760 x^{6} - 2640 x^{4} + 480 x^{2} - 32

e x p an d \frac{( x + 1 ) ( 6 x - 7 )}{( x + 3 ) ( x - 3 ) ( 3 x + 2 )}

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

e x p an d \frac{1}{( 3 n + 1 ) ^{15}}

s im pl i f y (2 - 1 - 4 x^{2})^{2}

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