erweitern-((6-x)^4)/(216)

Lösung

erweitern

- \frac{( 6 - x ) ^{4}}{216}

- \frac{x ^{4}}{216} + \frac{x ^{3}}{9} - x^{2} + 4 x - 6

Schritte zur Lösung

- \frac{( 6 - x ) ^{4}}{216}

(6 - x)^{4} = 1296 - 864 x + 216 x^{2} - 24 x^{3} + x^{4}

= - \frac{x ^{4} - 24 x ^{3} + 216 x ^{2} - 864 x + 1296}{216}

Wende Bruchregel an:

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

\frac{1296 - 864 x + 216 x ^{2} - 24 x ^{3} + x ^{4}}{216} = - (\frac{1296}{216}) - (- \frac{864 x}{216}) - (\frac{216 x ^{2}}{216}) - (- \frac{24 x ^{3}}{216}) - (\frac{x ^{4}}{216})

= - (\frac{1296}{216}) - (- \frac{864 x}{216}) - (\frac{216 x ^{2}}{216}) - (- \frac{24 x ^{3}}{216}) - (\frac{x ^{4}}{216})

Entferne die Klammern:

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

= - \frac{1296}{216} + \frac{864 x}{216} - \frac{216 x ^{2}}{216} + \frac{24 x ^{3}}{216} - \frac{x ^{4}}{216}

\frac{1296}{216} = 6

\frac{864 x}{216} = 4 x

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

\frac{24 x ^{3}}{216} = \frac{x ^{3}}{9}

= - 6 + 4 x - x^{2} + \frac{x ^{3}}{9} - \frac{x ^{4}}{216}

Rewrite in standard form

= - \frac{x ^{4}}{216} + \frac{x ^{3}}{9} - x^{2} + 4 x - 6

s im pl i f y (5 y + x) (5 y - 3 x)

e x p an d \frac{3 ( 1 - sin ( x ) )}{2 cos ( x )}

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

e x p an d 3 (x - 3)

e x p an d \frac{6 x + 13}{( x + 3 ) ( x + 2 )}