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

Lösung

erweitern

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

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

Schritte zur Lösung

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

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

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

Wende Bruchregel an:

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

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

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

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

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

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

\frac{16}{4} = 4

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

e x p an d \frac{727 ( - x + 3 )}{114}

e x p an d x \cdot (0.2 sin (0.3 t) + 0.6 cos (0.3 t))

e x p an d - \frac{6 ln ( 7 )}{35 ( 1 - e ^{\frac{l n ( 7 )}{35}} )}

s im pl i f y \frac{2197}{2000} (2 + lo g_{3} (2))

s im pl i f y (2 + i 3)^{4}