erweitern ((x-1)(x-2)(x-4)(x-5))/(40)

Lösung

erweitern

\frac{( x - 1 ) ( x - 2 ) ( x - 4 ) ( x - 5 )}{40}

\frac{x ^{4}}{40} - \frac{3 x ^{3}}{10} + \frac{49 x ^{2}}{40} - \frac{39 x}{20} + 1

Schritte zur Lösung

\frac{( x - 1 ) ( x - 2 ) ( x - 4 ) ( x - 5 )}{40}

Multipliziere aus

(x - 1) (x - 2) (x - 4) (x - 5) : x^{4} - 12 x^{3} + 49 x^{2} - 78 x + 40

= \frac{x ^{4} - 12 x ^{3} + 49 x ^{2} - 78 x + 40}{40}

Wende Bruchregel an:

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

\frac{x ^{4} - 12 x ^{3} + 49 x ^{2} - 78 x + 40}{40} = \frac{x ^{4}}{40} - \frac{12 x ^{3}}{40} + \frac{49 x ^{2}}{40} - \frac{78 x}{40} + \frac{40}{40}

= \frac{x ^{4}}{40} - \frac{12 x ^{3}}{40} + \frac{49 x ^{2}}{40} - \frac{78 x}{40} + \frac{40}{40}

Wende Regel an

\frac{a}{a} = 1

\frac{40}{40} = 1

= \frac{x ^{4}}{40} - \frac{12 x ^{3}}{40} + \frac{49 x ^{2}}{40} - \frac{78 x}{40} + 1

Streiche

\frac{12 x ^{3}}{40} : \frac{3 x ^{3}}{10}

= \frac{x ^{4}}{40} - \frac{3 x ^{3}}{10} + \frac{49 x ^{2}}{40} - \frac{78 x}{40} + 1

Streiche

\frac{78 x}{40} : \frac{39 x}{20}

= \frac{x ^{4}}{40} - \frac{3 x ^{3}}{10} + \frac{49 x ^{2}}{40} - \frac{39 x}{20} + 1

e x p an d \frac{4 x - 19}{4 ( x - 5 )}

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s im pl i f y (6 x + \frac{5}{x}) (2 x + 3)

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