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

Lösung

erweitern

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

64 x^{18} - 768 x^{16} + 960 x^{15} + 3840 x^{14} - 9600 x^{13} - 4240 x^{12} + 38400 x^{11} - 32640 x^{10} - 56800 x^{9} + 131712 x^{8} - 43200 x^{7} - 150404 x^{6} + 209280 x^{5} - 54000 x^{4} - 122500 x^{3} + 150000 x^{2} - 75000 x + 15625

Schritte zur Lösung

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

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

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

Multipliziere aus

(2 x^{3} - 4 x + 5) (2 x^{3} - 4 x + 5) (2 x^{3} - 4 x + 5) (2 x^{3} - 4 x + 5) (2 x^{3} - 4 x + 5) (2 x^{3} - 4 x + 5) : 64 x^{18} - 768 x^{16} + 960 x^{15} + 3840 x^{14} - 9600 x^{13} - 4240 x^{12} + 38400 x^{11} - 32640 x^{10} - 56800 x^{9} + 131712 x^{8} - 43200 x^{7} - 150404 x^{6} + 209280 x^{5} - 54000 x^{4} - 122500 x^{3} + 150000 x^{2} - 75000 x + 15625

= 64 x^{18} - 768 x^{16} + 960 x^{15} + 3840 x^{14} - 9600 x^{13} - 4240 x^{12} + 38400 x^{11} - 32640 x^{10} - 56800 x^{9} + 131712 x^{8} - 43200 x^{7} - 150404 x^{6} + 209280 x^{5} - 54000 x^{4} - 122500 x^{3} + 150000 x^{2} - 75000 x + 15625

e x p an d 4 sin (2) (π - θ)

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

e x p an d \frac{x ( x - 4 )}{( x + 6 ) ( x - 2 )}

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

e x p an d - \frac{2 ( 5 x ^{2} + 52 x - 34 )}{( x + 10 ) ( x + 1 ) ( x - 2 )}