erweitern ((2-x)^4)/4

Lösung

erweitern

\frac{( 2 - x ) ^{4}}{4}

\frac{x ^{4}}{4} - 2 x^{3} + 6 x^{2} - 8 x + 4

Schritte zur Lösung

\frac{( 2 - x ) ^{4}}{4}

(2 - x)^{4} = 16 - 32 x + 24 x^{2} - 8 x^{3} + x^{4}

= \frac{16 - 32 x + 24 x ^{2} - 8 x ^{3} + x ^{4}}{4}

Wende Bruchregel an:

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

\frac{16 - 32 x + 24 x ^{2} - 8 x ^{3} + x ^{4}}{4} = \frac{16}{4} - \frac{32 x}{4} + \frac{24 x ^{2}}{4} - \frac{8 x ^{3}}{4} + \frac{x ^{4}}{4}

= \frac{16}{4} - \frac{32 x}{4} + \frac{24 x ^{2}}{4} - \frac{8 x ^{3}}{4} + \frac{x ^{4}}{4}

\frac{16}{4} = 4

\frac{32 x}{4} = 8 x

\frac{24 x ^{2}}{4} = 6 x^{2}

\frac{8 x ^{3}}{4} = 2 x^{3}

= 4 - 8 x + 6 x^{2} - 2 x^{3} + \frac{x ^{4}}{4}

Rewrite in standard form

= \frac{x ^{4}}{4} - 2 x^{3} + 6 x^{2} - 8 x + 4

e x p an d (x + \frac{1}{x})^{9}

s im pl i f y m (m - 2)

e x p an d - \frac{4}{x ^{2} ( x - 2 )}

e x p an d (x^{2} + 4 y^{4} + 1) d x + 16 x y^{3} d y

e x p an d \frac{( x ^{7} + 1 )}{( x ^{2} + 1 ) ( x ^{2} + x + 1 )}