erweitern ((x-1)x^2(x+1)^2)/4

Lösung

erweitern

\frac{( x - 1 ) x ^{2} ( x + 1 ) ^{2}}{4}

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

Schritte zur Lösung

\frac{( x - 1 ) x ^{2} ( x + 1 ) ^{2}}{4}

(x + 1)^{2} = x^{2} + 2 x + 1

= \frac{x ^{2} ( x - 1 ) ( x ^{2} + 2 x + 1 )}{4}

Multipliziere aus

(x - 1) x^{2} (x^{2} + 2 x + 1) : x^{5} + x^{4} - x^{3} - x^{2}

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

Wende Bruchregel an:

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

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

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

s im pl i f y (4 - \frac{x ^{2}}{3}) (4 + \frac{x ^{2}}{3})

e x p an d \frac{( x ^{3} + 6 ) ^{2}}{225}

e x p an d \frac{8 x ^{2} - 6 x}{( 8 x - 3 ) ^{2}}

e x p an d 4 (5 x - 7 = 10 x + 2)

e x p an d \frac{1}{s ( s + 1 ) ( s + 5 ) ( s + 10 )}