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

Lösung

erweitern

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

- \frac{2 x ^{3}}{3} - \frac{4 x ^{2}}{3} - \frac{2 x}{3}

Schritte zur Lösung

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

(x + 1)^{2} = x^{2} + 2 x + 1

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

Multipliziere aus

2 x (x^{2} + 2 x + 1) : 2 x^{3} + 4 x^{2} + 2 x

= - \frac{2 x ^{3} + 4 x ^{2} + 2 x}{3}

Wende Bruchregel an:

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

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

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

Entferne die Klammern:

(a) = a

= - \frac{2 x ^{3}}{3} - \frac{4 x ^{2}}{3} - \frac{2 x}{3}

e x p an d 3 - sin (2 x^{2} - 3 x - 1) (4 x - 3)

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

e x p an d \frac{2 ( 2 n + 3 ) \cdot ( 5 n + 3 )}{3 ( 5 n + 8 ) \cdot ( 2 n + 1 )}

e x p an d f (x) (sin (\frac{x}{2}) = 2 + cos (x))

e x p an d x + 8 x + 16