erweitern ((x-1)(x-2)(x-5)*(x-6))/(60)

Lösung

erweitern

\frac{( x - 1 ) \cdot ( x - 2 ) \cdot ( x - 5 ) \cdot ( x - 6 )}{60}

\frac{x ^{4}}{60} - \frac{7 x ^{3}}{30} + \frac{13 x ^{2}}{12} - \frac{28 x}{15} + 1

Schritte zur Lösung

\frac{( x - 1 ) ( x - 2 ) ( x - 5 ) ( x - 6 )}{60}

Multipliziere aus

(x - 1) (x - 2) (x - 5) (x - 6) : x^{4} - 14 x^{3} + 65 x^{2} - 112 x + 60

= \frac{x ^{4} - 14 x ^{3} + 65 x ^{2} - 112 x + 60}{60}

Wende Bruchregel an:

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

\frac{x ^{4} - 14 x ^{3} + 65 x ^{2} - 112 x + 60}{60} = \frac{x ^{4}}{60} - \frac{14 x ^{3}}{60} + \frac{65 x ^{2}}{60} - \frac{112 x}{60} + \frac{60}{60}

= \frac{x ^{4}}{60} - \frac{14 x ^{3}}{60} + \frac{65 x ^{2}}{60} - \frac{112 x}{60} + \frac{60}{60}

Wende Regel an

\frac{a}{a} = 1

\frac{60}{60} = 1

= \frac{x ^{4}}{60} - \frac{14 x ^{3}}{60} + \frac{65 x ^{2}}{60} - \frac{112 x}{60} + 1

Streiche

\frac{14 x ^{3}}{60} : \frac{7 x ^{3}}{30}

= \frac{x ^{4}}{60} - \frac{7 x ^{3}}{30} + \frac{65 x ^{2}}{60} - \frac{112 x}{60} + 1

Streiche

\frac{65 x ^{2}}{60} : \frac{13 x ^{2}}{12}

= \frac{x ^{4}}{60} - \frac{7 x ^{3}}{30} + \frac{13 x ^{2}}{12} - \frac{112 x}{60} + 1

Streiche

\frac{112 x}{60} : \frac{28 x}{15}

= \frac{x ^{4}}{60} - \frac{7 x ^{3}}{30} + \frac{13 x ^{2}}{12} - \frac{28 x}{15} + 1

s im pl i f y (2 - x - 3) (2 + x - 3)

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

e x p an d (ln (x)) (5 x^{2} - 3)

e x p an d \frac{x ^{5} - 3 x ^{2} + 12 x - 1}{x ^{3} ( x ^{2} + x + 1 ) ( x + 2 ) ^{3}}

e x p an d (- 2 sin (x) - sin (2 x) \cdot 2)^{2}