erweitern-(4(-x+3)^4)/(27)

Lösung

erweitern

- \frac{4 ( - x + 3 ) ^{4}}{27}

- \frac{4 x ^{4}}{27} + \frac{16 x ^{3}}{9} - 8 x^{2} + 16 x - 12

Schritte zur Lösung

- \frac{4 ( - x + 3 ) ^{4}}{27}

(- x + 3)^{4} = x^{4} - 12 x^{3} + 54 x^{2} - 108 x + 81

= - \frac{4 ( x ^{4} - 12 x ^{3} + 54 x ^{2} - 108 x + 81 )}{27}

Multipliziere aus

4 (x^{4} - 12 x^{3} + 54 x^{2} - 108 x + 81) : 4 x^{4} - 48 x^{3} + 216 x^{2} - 432 x + 324

= - \frac{4 x ^{4} - 48 x ^{3} + 216 x ^{2} - 432 x + 324}{27}

Wende Bruchregel an:

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

\frac{4 x ^{4} - 48 x ^{3} + 216 x ^{2} - 432 x + 324}{27} = - (\frac{4 x ^{4}}{27}) - (- \frac{48 x ^{3}}{27}) - (\frac{216 x ^{2}}{27}) - (- \frac{432 x}{27}) - (\frac{324}{27})

= - (\frac{4 x ^{4}}{27}) - (- \frac{48 x ^{3}}{27}) - (\frac{216 x ^{2}}{27}) - (- \frac{432 x}{27}) - (\frac{324}{27})

Entferne die Klammern:

(a) = a, - (- a) = a

= - \frac{4 x ^{4}}{27} + \frac{48 x ^{3}}{27} - \frac{216 x ^{2}}{27} + \frac{432 x}{27} - \frac{324}{27}

\frac{48 x ^{3}}{27} = \frac{16 x ^{3}}{9}

\frac{216 x ^{2}}{27} = 8 x^{2}

\frac{432 x}{27} = 16 x

\frac{324}{27} = 12

= - \frac{4 x ^{4}}{27} + \frac{16 x ^{3}}{9} - 8 x^{2} + 16 x - 12

e x p an d (1 - e^{- \frac{y}{8}})^{3}

e x p an d π (1 - x^{2})^{2}

\frac{d}{d t} ((x) (x - 2 y))

e x p an d \frac{k}{( a - x ) ( b - x )}

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