erweitern-(x^2(-x+3)^2)/(18)

Lösung

erweitern

- \frac{x ^{2} ( - x + 3 ) ^{2}}{18}

- \frac{x ^{4}}{18} + \frac{x ^{3}}{3} - \frac{x ^{2}}{2}

Schritte zur Lösung

- \frac{x ^{2} ( - x + 3 ) ^{2}}{18}

(- x + 3)^{2} = x^{2} - 6 x + 9

= - \frac{x ^{2} ( x ^{2} - 6 x + 9 )}{18}

Multipliziere aus

x^{2} (x^{2} - 6 x + 9) : x^{4} - 6 x^{3} + 9 x^{2}

= - \frac{x ^{4} - 6 x ^{3} + 9 x ^{2}}{18}

Wende Bruchregel an:

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

\frac{x ^{4} - 6 x ^{3} + 9 x ^{2}}{18} = - (\frac{x ^{4}}{18}) - (- \frac{6 x ^{3}}{18}) - (\frac{9 x ^{2}}{18})

= - (\frac{x ^{4}}{18}) - (- \frac{6 x ^{3}}{18}) - (\frac{9 x ^{2}}{18})

Entferne die Klammern:

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

= - \frac{x ^{4}}{18} + \frac{6 x ^{3}}{18} - \frac{9 x ^{2}}{18}

Streiche

\frac{6 x ^{3}}{18} : \frac{x ^{3}}{3}

= - \frac{x ^{4}}{18} + \frac{x ^{3}}{3} - \frac{9 x ^{2}}{18}

Streiche

\frac{9 x ^{2}}{18} : \frac{x ^{2}}{2}

= - \frac{x ^{4}}{18} + \frac{x ^{3}}{3} - \frac{x ^{2}}{2}

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