erweitern ((2x-1)^3)/x

Lösung

erweitern

\frac{( 2 x - 1 ) ^{3}}{x}

8 x^{2} - 12 x + 6 - \frac{1}{x}

Schritte zur Lösung

\frac{( 2 x - 1 ) ^{3}}{x}

(2 x - 1)^{3} = 8 x^{3} - 12 x^{2} + 6 x - 1

= \frac{8 x ^{3} - 12 x ^{2} + 6 x - 1}{x}

Wende Bruchregel an:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{8 x ^{3} - 12 x ^{2} + 6 x - 1}{x} = \frac{8 x ^{3}}{x} - \frac{12 x ^{2}}{x} + \frac{6 x}{x} - \frac{1}{x}

= \frac{8 x ^{3}}{x} - \frac{12 x ^{2}}{x} + \frac{6 x}{x} - \frac{1}{x}

Streiche

\frac{8 x ^{3}}{x} : 8 x^{2}

= 8 x^{2} - \frac{12 x ^{2}}{x} + \frac{6 x}{x} - \frac{1}{x}

Streiche

\frac{12 x ^{2}}{x} : 12 x

= 8 x^{2} - 12 x + \frac{6 x}{x} - \frac{1}{x}

Streiche

\frac{6 x}{x} : 6

= 8 x^{2} - 12 x + 6 - \frac{1}{x}

e x p an d ln (1 + x) (2 (1 + x)^{2})

e x p an d (a x + b) e^{x}

e x p an d (y^{2} - x y) d x + x^{2} d y

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

e x p an d \frac{1}{2} ((8, - 1) - (- 2, 5))