erweitern ((2n+3x)^3)/(n^4)

Lösung

erweitern

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

\frac{8}{n} + \frac{36 x}{n ^{2}} + \frac{54 x ^{2}}{n ^{3}} + \frac{27 x ^{3}}{n ^{4}}

Schritte zur Lösung

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

(2 n + 3 x)^{3} = 8 n^{3} + 36 n^{2} x + 54 n x^{2} + 27 x^{3}

= \frac{8 n ^{3} + 36 n ^{2} x + 54 n x ^{2} + 27 x ^{3}}{n ^{4}}

Wende Bruchregel an:

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

\frac{8 n ^{3} + 36 n ^{2} x + 54 n x ^{2} + 27 x ^{3}}{n ^{4}} = \frac{8 n ^{3}}{n ^{4}} + \frac{36 n ^{2} x}{n ^{4}} + \frac{54 n x ^{2}}{n ^{4}} + \frac{27 x ^{3}}{n ^{4}}

= \frac{8 n ^{3}}{n ^{4}} + \frac{36 n ^{2} x}{n ^{4}} + \frac{54 n x ^{2}}{n ^{4}} + \frac{27 x ^{3}}{n ^{4}}

Streiche

\frac{8 n ^{3}}{n ^{4}} : \frac{8}{n}

= \frac{8}{n} + \frac{36 n ^{2} x}{n ^{4}} + \frac{54 n x ^{2}}{n ^{4}} + \frac{27 x ^{3}}{n ^{4}}

Streiche

\frac{36 n ^{2} x}{n ^{4}} : \frac{36 x}{n ^{2}}

= \frac{8}{n} + \frac{36 x}{n ^{2}} + \frac{54 n x ^{2}}{n ^{4}} + \frac{27 x ^{3}}{n ^{4}}

Streiche

\frac{54 n x ^{2}}{n ^{4}} : \frac{54 x ^{2}}{n ^{3}}

= \frac{8}{n} + \frac{36 x}{n ^{2}} + \frac{54 x ^{2}}{n ^{3}} + \frac{27 x ^{3}}{n ^{4}}

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