erweitern (k^2(k+1)^2)/4+(k+1)

Lösung

erweitern

\frac{k ^{2} ( k + 1 ) ^{2}}{4} + (k + 1)

\frac{k ^{4}}{4} + \frac{k ^{3}}{2} + \frac{k ^{2}}{4} + k + 1

Schritte zur Lösung

\frac{k ^{2} ( k + 1 ) ^{2}}{4} + (k + 1)

Entferne die Klammern:

(a) = a

= \frac{k ^{2} ( k + 1 ) ^{2}}{4} + k + 1

\frac{k ^{2} ( k + 1 ) ^{2}}{4} = \frac{k ^{4} + 2 k ^{3} + k ^{2}}{4}

= \frac{k ^{4} + 2 k ^{3} + k ^{2}}{4} + k + 1

Wende Bruchregel an:

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

\frac{k ^{4} + 2 k ^{3} + k ^{2}}{4} = \frac{k ^{4}}{4} + \frac{2 k ^{3}}{4} + \frac{k ^{2}}{4}

= \frac{k ^{4}}{4} + \frac{2 k ^{3}}{4} + \frac{k ^{2}}{4} + k + 1

Streiche

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

= \frac{k ^{4}}{4} + \frac{k ^{3}}{2} + \frac{k ^{2}}{4} + k + 1

e x p an d \frac{3 - x}{4 ( x + 1 ) ^{k}}

e x p an d \frac{( ( - x + 9 ) ( x - 3 ) )}{2}

e x p an d \frac{π}{32} \cdot ((0.051)^{4} - (0, 41)^{4})

e x p an d \frac{( 2 - 3 x ^{2} ) ^{5}}{5 x}

e x p an d (1 + 4 sin (t)) (4 cos (t))