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Beliebt Algebra >

erweitern-(a^2(-5a^2b^4-6ac+7c^3))/(b^2c)

Lösung

erweitern

- \frac{a ^{2} ( - 5 a ^{2} b ^{4} - 6 a c + 7 c ^{3} )}{b ^{2} c}

Lösung

\frac{5 a ^{4} b ^{2}}{c} + \frac{6 a ^{3}}{b ^{2}} - \frac{7 a ^{2} c ^{2}}{b ^{2}}

Schritte zur Lösung

- \frac{a ^{2} ( - 5 a ^{2} b ^{4} - 6 a c + 7 c ^{3} )}{b ^{2} c}

Multipliziere aus

a^{2} (- 5 a^{2} b^{4} - 6 a c + 7 c^{3}) : - 5 a^{4} b^{4} - 6 a^{3} c + 7 a^{2} c^{3}

= - \frac{- 5 a ^{4} b ^{4} - 6 a ^{3} c + 7 a ^{2} c ^{3}}{b ^{2} c}

Wende Bruchregel an:

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

\frac{- 5 a ^{4} b ^{4} - 6 a ^{3} c + 7 a ^{2} c ^{3}}{b ^{2} c} = - (- \frac{5 a ^{4} b ^{4}}{b ^{2} c}) - (- \frac{6 a ^{3} c}{b ^{2} c}) - (\frac{7 a ^{2} c ^{3}}{b ^{2} c})

= - (- \frac{5 a ^{4} b ^{4}}{b ^{2} c}) - (- \frac{6 a ^{3} c}{b ^{2} c}) - (\frac{7 a ^{2} c ^{3}}{b ^{2} c})

Entferne die Klammern:

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

= \frac{5 a ^{4} b ^{4}}{b ^{2} c} + \frac{6 a ^{3} c}{b ^{2} c} - \frac{7 a ^{2} c ^{3}}{b ^{2} c}

Streiche

\frac{5 a ^{4} b ^{4}}{b ^{2} c} : \frac{5 a ^{4} b ^{2}}{c}

= \frac{5 a ^{4} b ^{2}}{c} + \frac{6 a ^{3} c}{b ^{2} c} - \frac{7 a ^{2} c ^{3}}{b ^{2} c}

Streiche

\frac{6 a ^{3} c}{b ^{2} c} : \frac{6 a ^{3}}{b ^{2}}

= \frac{5 a ^{4} b ^{2}}{c} + \frac{6 a ^{3}}{b ^{2}} - \frac{7 a ^{2} c ^{3}}{b ^{2} c}

Streiche

\frac{7 a ^{2} c ^{3}}{b ^{2} c} : \frac{7 a ^{2} c ^{2}}{b ^{2}}

= \frac{5 a ^{4} b ^{2}}{c} + \frac{6 a ^{3}}{b ^{2}} - \frac{7 a ^{2} c ^{2}}{b ^{2}}

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