erweitern ((3x+7)^3)/(9261)

Lösung

erweitern

\frac{( 3 x + 7 ) ^{3}}{9261}

\frac{x ^{3}}{343} + \frac{x ^{2}}{49} + \frac{x}{21} + \frac{1}{27}

Schritte zur Lösung

\frac{( 3 x + 7 ) ^{3}}{9261}

(3 x + 7)^{3} = 27 x^{3} + 189 x^{2} + 441 x + 343

= \frac{27 x ^{3} + 189 x ^{2} + 441 x + 343}{9261}

Wende Bruchregel an:

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

\frac{27 x ^{3} + 189 x ^{2} + 441 x + 343}{9261} = \frac{27 x ^{3}}{9261} + \frac{189 x ^{2}}{9261} + \frac{441 x}{9261} + \frac{343}{9261}

= \frac{27 x ^{3}}{9261} + \frac{189 x ^{2}}{9261} + \frac{441 x}{9261} + \frac{343}{9261}

\frac{27 x ^{3}}{9261} = \frac{x ^{3}}{343}

\frac{189 x ^{2}}{9261} = \frac{x ^{2}}{49}

\frac{441 x}{9261} = \frac{x}{21}

\frac{343}{9261} = \frac{1}{27}

= \frac{x ^{3}}{343} + \frac{x ^{2}}{49} + \frac{x}{21} + \frac{1}{27}

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