erweitern ((x-0)(x-1)(x-5)(x-6))/(24)

Lösung

erweitern

\frac{( x - 0 ) ( x - 1 ) ( x - 5 ) ( x - 6 )}{24}

\frac{x ^{4}}{24} - \frac{x ^{3}}{2} + \frac{41 x ^{2}}{24} - \frac{5 x}{4}

Schritte zur Lösung

\frac{( x - 0 ) ( x - 1 ) ( x - 5 ) ( x - 6 )}{24}

x - 0 = x

= \frac{x ( x - 1 ) ( x - 5 ) ( x - 6 )}{24}

Multipliziere aus

x (x - 1) (x - 5) (x - 6) : x^{4} - 12 x^{3} + 41 x^{2} - 30 x

= \frac{x ^{4} - 12 x ^{3} + 41 x ^{2} - 30 x}{24}

Wende Bruchregel an:

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

\frac{x ^{4} - 12 x ^{3} + 41 x ^{2} - 30 x}{24} = \frac{x ^{4}}{24} - \frac{12 x ^{3}}{24} + \frac{41 x ^{2}}{24} - \frac{30 x}{24}

= \frac{x ^{4}}{24} - \frac{12 x ^{3}}{24} + \frac{41 x ^{2}}{24} - \frac{30 x}{24}

Streiche

\frac{12 x ^{3}}{24} : \frac{x ^{3}}{2}

= \frac{x ^{4}}{24} - \frac{x ^{3}}{2} + \frac{41 x ^{2}}{24} - \frac{30 x}{24}

Streiche

\frac{30 x}{24} : \frac{5 x}{4}

= \frac{x ^{4}}{24} - \frac{x ^{3}}{2} + \frac{41 x ^{2}}{24} - \frac{5 x}{4}

e x p an d y (y^{2} + 1) d x + x (y^{2} - 1) d y

e x p an d 10 (a^{100})

e x p an d 81

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

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