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

Lösung

erweitern

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

1 - \frac{11 x}{2 L} + \frac{9 x ^{2}}{L ^{2}} - \frac{9 x ^{3}}{2 L ^{3}}

Schritte zur Lösung

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

Multipliziere aus

(- L + 3 x) (- 2 L + 3 x) (- L + x) : - 2 L^{3} + 11 L^{2} x - 18 L x^{2} + 9 x^{3}

= - \frac{- 2 L ^{3} + 11 L ^{2} x - 18 L x ^{2} + 9 x ^{3}}{2 L ^{3}}

Wende Bruchregel an:

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

\frac{- 2 L ^{3} + 11 L ^{2} x - 18 L x ^{2} + 9 x ^{3}}{2 L ^{3}} = - (- \frac{2 L ^{3}}{2 L ^{3}}) - (\frac{11 L ^{2} x}{2 L ^{3}}) - (- \frac{18 L x ^{2}}{2 L ^{3}}) - (\frac{9 x ^{3}}{2 L ^{3}})

= - (- \frac{2 L ^{3}}{2 L ^{3}}) - (\frac{11 L ^{2} x}{2 L ^{3}}) - (- \frac{18 L x ^{2}}{2 L ^{3}}) - (\frac{9 x ^{3}}{2 L ^{3}})

Entferne die Klammern:

(a) = a, - (- a) = a

= \frac{2 L ^{3}}{2 L ^{3}} - \frac{11 L ^{2} x}{2 L ^{3}} + \frac{18 L x ^{2}}{2 L ^{3}} - \frac{9 x ^{3}}{2 L ^{3}}

Wende Regel an

\frac{a}{a} = 1

= 1 - \frac{11 L ^{2} x}{2 L ^{3}} + \frac{18 L x ^{2}}{2 L ^{3}} - \frac{9 x ^{3}}{2 L ^{3}}

Streiche

\frac{11 L ^{2} x}{2 L ^{3}} : \frac{11 x}{2 L}

= 1 - \frac{11 x}{2 L} + \frac{18 L x ^{2}}{2 L ^{3}} - \frac{9 x ^{3}}{2 L ^{3}}

Streiche

\frac{18 L x ^{2}}{2 L ^{3}} : \frac{9 x ^{2}}{L ^{2}}

= 1 - \frac{11 x}{2 L} + \frac{9 x ^{2}}{L ^{2}} - \frac{9 x ^{3}}{2 L ^{3}}

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