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

Lösung

erweitern

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

\frac{8}{n} + \frac{12 k}{n ^{2}} + \frac{6 k ^{2}}{n ^{3}} + \frac{k ^{3}}{n ^{4}}

Schritte zur Lösung

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

(2 n + k)^{3} = 8 n^{3} + 12 n^{2} k + 6 n k^{2} + k^{3}

= \frac{8 n ^{3} + 12 n ^{2} k + 6 n k ^{2} + k ^{3}}{n ^{4}}

Wende Bruchregel an:

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

\frac{8 n ^{3} + 12 n ^{2} k + 6 n k ^{2} + k ^{3}}{n ^{4}} = \frac{8 n ^{3}}{n ^{4}} + \frac{12 n ^{2} k}{n ^{4}} + \frac{6 n k ^{2}}{n ^{4}} + \frac{k ^{3}}{n ^{4}}

= \frac{8 n ^{3}}{n ^{4}} + \frac{12 n ^{2} k}{n ^{4}} + \frac{6 n k ^{2}}{n ^{4}} + \frac{k ^{3}}{n ^{4}}

Streiche

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

= \frac{8}{n} + \frac{12 n ^{2} k}{n ^{4}} + \frac{6 n k ^{2}}{n ^{4}} + \frac{k ^{3}}{n ^{4}}

Streiche

\frac{12 n ^{2} k}{n ^{4}} : \frac{12 k}{n ^{2}}

= \frac{8}{n} + \frac{12 k}{n ^{2}} + \frac{6 n k ^{2}}{n ^{4}} + \frac{k ^{3}}{n ^{4}}

Streiche

\frac{6 n k ^{2}}{n ^{4}} : \frac{6 k ^{2}}{n ^{3}}

= \frac{8}{n} + \frac{12 k}{n ^{2}} + \frac{6 k ^{2}}{n ^{3}} + \frac{k ^{3}}{n ^{4}}

e x p an d (k + 2)!

e x p an d (3 x^{2} - 7 x + 4)^{8}

e x p an d \frac{h x + d}{( x - r ) ^{2}}

e x p an d \frac{11 π}{45 3}

e x p an d 1.07466494 \cdot 1 0^{9}