erweitern ((4-x)^3)/(64)

Lösung

erweitern

\frac{( 4 - x ) ^{3}}{64}

- \frac{x ^{3}}{64} + \frac{3 x ^{2}}{16} - \frac{3 x}{4} + 1

Schritte zur Lösung

\frac{( 4 - x ) ^{3}}{64}

(4 - x)^{3} = 64 - 48 x + 12 x^{2} - x^{3}

= \frac{64 - 48 x + 12 x ^{2} - x ^{3}}{64}

Wende Bruchregel an:

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

\frac{64 - 48 x + 12 x ^{2} - x ^{3}}{64} = \frac{64}{64} - \frac{48 x}{64} + \frac{12 x ^{2}}{64} - \frac{x ^{3}}{64}

= \frac{64}{64} - \frac{48 x}{64} + \frac{12 x ^{2}}{64} - \frac{x ^{3}}{64}

Wende Regel an

\frac{a}{a} = 1

\frac{64}{64} = 1

= 1 - \frac{48 x}{64} + \frac{12 x ^{2}}{64} - \frac{x ^{3}}{64}

Streiche

\frac{48 x}{64} : \frac{3 x}{4}

= 1 - \frac{3 x}{4} + \frac{12 x ^{2}}{64} - \frac{x ^{3}}{64}

Streiche

\frac{12 x ^{2}}{64} : \frac{3 x ^{2}}{16}

= 1 - \frac{3 x}{4} + \frac{3 x ^{2}}{16} - \frac{x ^{3}}{64}

Rewrite in standard form

= - \frac{x ^{3}}{64} + \frac{3 x ^{2}}{16} - \frac{3 x}{4} + 1

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

e x p an d \frac{5 x}{2 ( x - 3 )}

e x p an d (2 n - 1) (2 n +!)

e x p an d \frac{( u + 3 ) ( 5 u + 1 )}{10 u ^{2} - 11 u + 1}

s im pl i f y (- 4 x + 1) (x - 5)