erweitern (x^2(8-x)^3)/(24)

Lösung

erweitern

\frac{x ^{2} ( 8 - x ) ^{3}}{24}

- \frac{x ^{5}}{24} + x^{4} - 8 x^{3} + \frac{64 x ^{2}}{3}

Schritte zur Lösung

\frac{x ^{2} ( 8 - x ) ^{3}}{24}

(8 - x)^{3} = 512 - 192 x + 24 x^{2} - x^{3}

= \frac{x ^{2} ( - x ^{3} + 24 x ^{2} - 192 x + 512 )}{24}

Multipliziere aus

x^{2} (512 - 192 x + 24 x^{2} - x^{3}) : 512 x^{2} - 192 x^{3} + 24 x^{4} - x^{5}

= \frac{512 x ^{2} - 192 x ^{3} + 24 x ^{4} - x ^{5}}{24}

Wende Bruchregel an:

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

\frac{512 x ^{2} - 192 x ^{3} + 24 x ^{4} - x ^{5}}{24} = \frac{512 x ^{2}}{24} - \frac{192 x ^{3}}{24} + \frac{24 x ^{4}}{24} - \frac{x ^{5}}{24}

= \frac{512 x ^{2}}{24} - \frac{192 x ^{3}}{24} + \frac{24 x ^{4}}{24} - \frac{x ^{5}}{24}

Streiche

\frac{512 x ^{2}}{24} : \frac{64 x ^{2}}{3}

= \frac{64 x ^{2}}{3} - \frac{192 x ^{3}}{24} + \frac{24 x ^{4}}{24} - \frac{x ^{5}}{24}

Teile die Zahlen:

\frac{192}{24} = 8

= \frac{64 x ^{2}}{3} - 8 x^{3} + \frac{24 x ^{4}}{24} - \frac{x ^{5}}{24}

Teile die Zahlen:

\frac{24}{24} = 1

= \frac{64 x ^{2}}{3} - 8 x^{3} + x^{4} - \frac{x ^{5}}{24}

Rewrite in standard form

= - \frac{x ^{5}}{24} + x^{4} - 8 x^{3} + \frac{64 x ^{2}}{3}

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

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

e x p an d \frac{4 ( x + h ) - 5 - ( 4 ( x ) - 5 )}{h}

e x p an d \frac{180 ( x - 2 )}{x}

e x p an d \frac{4 ^{n + 1} + ( n + 1 ) ^{2}}{4 ^{n} + n ^{2}}