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

Lösung

erweitern

\frac{( - 2 x + 2 ) ( - x ^{2} + 2 x - 4 )}{( x ^{2} - 2 x ) ^{3}}

\frac{2 x ^{3} - 6 x ^{2} + 12 x - 8}{x ^{6} - 6 x ^{5} + 12 x ^{4} - 8 x ^{3}}

Schritte zur Lösung

\frac{( - 2 x + 2 ) ( - x ^{2} + 2 x - 4 )}{( x ^{2} - 2 x ) ^{3}}

(x^{2} - 2 x)^{3} = x^{6} - 6 x^{5} + 12 x^{4} - 8 x^{3}

= \frac{( - 2 x + 2 ) ( - x ^{2} + 2 x - 4 )}{x ^{6} - 6 x ^{5} + 12 x ^{4} - 8 x ^{3}}

Multipliziere aus

(- 2 x + 2) (- x^{2} + 2 x - 4) : 2 x^{3} - 6 x^{2} + 12 x - 8

= \frac{2 x ^{3} - 6 x ^{2} + 12 x - 8}{x ^{6} - 6 x ^{5} + 12 x ^{4} - 8 x ^{3}}

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

e x p an d (y = 3, x - 1) (y = 2 x - 4)

e x p an d \frac{8 - 10 x}{5}

e x p an d \frac{2 ( 3 + a )}{b}

e x p an d 2 π (y + 5) (1 - y)