erweitern ((k-1)(3k^6-k^5-k^4+k^3+k^2+k+1))/(k^4)

Lösung

erweitern

\frac{( k - 1 ) ( 3 k ^{6} - k ^{5} - k ^{4} + k ^{3} + k ^{2} + k + 1 )}{k ^{4}}

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

Schritte zur Lösung

\frac{( k - 1 ) ( 3 k ^{6} - k ^{5} - k ^{4} + k ^{3} + k ^{2} + k + 1 )}{k ^{4}}

Multipliziere aus

(k - 1) (3 k^{6} - k^{5} - k^{4} + k^{3} + k^{2} + k + 1) : 3 k^{7} - 4 k^{6} + 2 k^{4} - 1

= \frac{3 k ^{7} - 4 k ^{6} + 2 k ^{4} - 1}{k ^{4}}

Wende Bruchregel an:

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

\frac{3 k ^{7} - 4 k ^{6} + 2 k ^{4} - 1}{k ^{4}} = \frac{3 k ^{7}}{k ^{4}} - \frac{4 k ^{6}}{k ^{4}} + \frac{2 k ^{4}}{k ^{4}} - \frac{1}{k ^{4}}

= \frac{3 k ^{7}}{k ^{4}} - \frac{4 k ^{6}}{k ^{4}} + \frac{2 k ^{4}}{k ^{4}} - \frac{1}{k ^{4}}

Streiche

\frac{3 k ^{7}}{k ^{4}} : 3 k^{3}

= 3 k^{3} - \frac{4 k ^{6}}{k ^{4}} + \frac{2 k ^{4}}{k ^{4}} - \frac{1}{k ^{4}}

Streiche

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

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

Streiche

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

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

e x p an d \frac{2 sin ( x ) - sin ( 2 x )}{2 cos ( x ) ( 1 - cos ( x ) )}

e x p an d (5 x + 8 x^{3} - x^{2} + 9) l e f t (4 x - 5)

e x p an d \frac{2 e ^{- 5 s}}{s ( 3 s + 1 )}

e x p an d (3 + (- 5 x)) y^{''} (x) + (5 x) y^{'} (x) + 3 y

e x p an d (r^{2} + 5 r) (34 - 5 + r)