erweitern ((5x-8)^2x(3+x)(3-x))/(25)

Lösung

erweitern

\frac{( 5 x - 8 ) ^{2} x ( 3 + x ) ( 3 - x )}{25}

- x^{5} + \frac{16 x ^{4}}{5} + \frac{161 x ^{3}}{25} - \frac{144 x ^{2}}{5} + \frac{576 x}{25}

Schritte zur Lösung

\frac{( 5 x - 8 ) ^{2} x ( 3 + x ) ( 3 - x )}{25}

(5 x - 8)^{2} = 25 x^{2} - 80 x + 64

= \frac{x ( 25 x ^{2} - 80 x + 64 ) ( x + 3 ) ( - x + 3 )}{25}

Multipliziere aus

(25 x^{2} - 80 x + 64) x (3 + x) (3 - x) : - 25 x^{5} + 80 x^{4} + 161 x^{3} - 720 x^{2} + 576 x

= \frac{- 25 x ^{5} + 80 x ^{4} + 161 x ^{3} - 720 x ^{2} + 576 x}{25}

Wende Bruchregel an:

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

\frac{- 25 x ^{5} + 80 x ^{4} + 161 x ^{3} - 720 x ^{2} + 576 x}{25} = - \frac{25 x ^{5}}{25} + \frac{80 x ^{4}}{25} + \frac{161 x ^{3}}{25} - \frac{720 x ^{2}}{25} + \frac{576 x}{25}

= - \frac{25 x ^{5}}{25} + \frac{80 x ^{4}}{25} + \frac{161 x ^{3}}{25} - \frac{720 x ^{2}}{25} + \frac{576 x}{25}

Teile die Zahlen:

\frac{25}{25} = 1

= - x^{5} + \frac{80 x ^{4}}{25} + \frac{161 x ^{3}}{25} - \frac{720 x ^{2}}{25} + \frac{576 x}{25}

Streiche

\frac{80 x ^{4}}{25} : \frac{16 x ^{4}}{5}

= - x^{5} + \frac{16 x ^{4}}{5} + \frac{161 x ^{3}}{25} - \frac{720 x ^{2}}{25} + \frac{576 x}{25}

Streiche

\frac{720 x ^{2}}{25} : \frac{144 x ^{2}}{5}

= - x^{5} + \frac{16 x ^{4}}{5} + \frac{161 x ^{3}}{25} - \frac{144 x ^{2}}{5} + \frac{576 x}{25}

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