erweitern (k(2n+1-2k))/(n^2)

Lösung

erweitern

\frac{k ( 2 n + 1 - 2 k )}{n ^{2}}

\frac{2 k}{n} + \frac{k}{n ^{2}} - \frac{2 k ^{2}}{n ^{2}}

Schritte zur Lösung

\frac{k ( 2 n + 1 - 2 k )}{n ^{2}}

Multipliziere aus

k (2 n + 1 - 2 k) : 2 kn + k - 2 k^{2}

= \frac{2 kn + k - 2 k ^{2}}{n ^{2}}

Wende Bruchregel an:

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

\frac{2 kn + k - 2 k ^{2}}{n ^{2}} = \frac{2 kn}{n ^{2}} + \frac{k}{n ^{2}} - \frac{2 k ^{2}}{n ^{2}}

= \frac{2 kn}{n ^{2}} + \frac{k}{n ^{2}} - \frac{2 k ^{2}}{n ^{2}}

Streiche

\frac{2 kn}{n ^{2}} : \frac{2 k}{n}

= \frac{2 k}{n} + \frac{k}{n ^{2}} - \frac{2 k ^{2}}{n ^{2}}

e x p an d (2 x + e^{x}) (x^{3} + 2 e^{x})

e x p an d \frac{( 4 x + 9 )}{( x + 3 ) ( x - 3 )}

e x p an d (2, - 6, 4) x (- 1, 3, 5)

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

e x p an d det (λ - 1) (λ^{2} - 2 λ - 2)