erweitern ((x-4)^2(125x-500))/(18)

Lösung

erweitern

\frac{( x - 4 ) ^{2} ( 125 x - 500 )}{18}

\frac{125 x ^{3}}{18} - \frac{250 x ^{2}}{3} + \frac{1000 x}{3} - \frac{4000}{9}

Schritte zur Lösung

\frac{( x - 4 ) ^{2} ( 125 x - 500 )}{18}

(x - 4)^{2} = x^{2} - 8 x + 16

= \frac{( x ^{2} - 8 x + 16 ) ( 125 x - 500 )}{18}

Multipliziere aus

(x^{2} - 8 x + 16) (125 x - 500) : 125 x^{3} - 1500 x^{2} + 6000 x - 8000

= \frac{125 x ^{3} - 1500 x ^{2} + 6000 x - 8000}{18}

Wende Bruchregel an:

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

\frac{125 x ^{3} - 1500 x ^{2} + 6000 x - 8000}{18} = \frac{125 x ^{3}}{18} - \frac{1500 x ^{2}}{18} + \frac{6000 x}{18} - \frac{8000}{18}

= \frac{125 x ^{3}}{18} - \frac{1500 x ^{2}}{18} + \frac{6000 x}{18} - \frac{8000}{18}

Streiche

\frac{1500 x ^{2}}{18} : \frac{250 x ^{2}}{3}

= \frac{125 x ^{3}}{18} - \frac{250 x ^{2}}{3} + \frac{6000 x}{18} - \frac{8000}{18}

Streiche

\frac{6000 x}{18} : \frac{1000 x}{3}

= \frac{125 x ^{3}}{18} - \frac{250 x ^{2}}{3} + \frac{1000 x}{3} - \frac{8000}{18}

Streiche

\frac{8000}{18} : \frac{4000}{9}

= \frac{125 x ^{3}}{18} - \frac{250 x ^{2}}{3} + \frac{1000 x}{3} - \frac{4000}{9}

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