erweitern (x^3-2x^2+1/2)^3

Lösung

erweitern

(x^{3} - 2 x^{2} + \frac{1}{2})^{3}

x^{9} - 6 x^{8} + 12 x^{7} - \frac{13 x ^{6}}{2} - 6 x^{5} + 6 x^{4} - \frac{3 x ^{2}}{2} + \frac{3 x ^{3}}{4} + \frac{1}{8}

Schritte zur Lösung

(x^{3} - 2 x^{2} + \frac{1}{2})^{3}

Vereinfache

(x^{3} - 2 x^{2} + \frac{1}{2})^{3} : (x^{3} - 2 x^{2} + \frac{1}{2}) (x^{3} - 2 x^{2} + \frac{1}{2}) (x^{3} - 2 x^{2} + \frac{1}{2})

= (x^{3} - 2 x^{2} + \frac{1}{2}) (x^{3} - 2 x^{2} + \frac{1}{2}) (x^{3} - 2 x^{2} + \frac{1}{2})

Schreibe

(x^{3} - 2 x^{2} + \frac{1}{2}) (x^{3} - 2 x^{2} + \frac{1}{2})

um:

x^{6} - 4 x^{5} + 4 x^{4} + x^{3} - 2 x^{2} + \frac{1}{4}

= (x^{6} - 4 x^{5} + 4 x^{4} + x^{3} - 2 x^{2} + \frac{1}{4}) (x^{3} - 2 x^{2} + \frac{1}{2})

Setze Klammern

= x^{6} x^{3} + x^{6} (- 2 x^{2}) + x^{6} \frac{1}{2} - 4 x^{5} x^{3} - 4 x^{5} (- 2 x^{2}) - 4 x^{5} \frac{1}{2} + 4 x^{4} x^{3} + 4 x^{4} (- 2 x^{2}) + 4 x^{4} \frac{1}{2} + x^{3} x^{3} + x^{3} (- 2 x^{2}) + x^{3} \frac{1}{2} - 2 x^{2} x^{3} - 2 x^{2} (- 2 x^{2}) - 2 x^{2} \frac{1}{2} + \frac{1}{4} x^{3} + \frac{1}{4} (- 2 x^{2}) + \frac{1}{4} \cdot \frac{1}{2}

Vereinfache

x^{6} x^{3} + x^{6} (- 2 x^{2}) + x^{6} \frac{1}{2} - 4 x^{5} x^{3} - 4 x^{5} (- 2 x^{2}) - 4 x^{5} \frac{1}{2} + 4 x^{4} x^{3} + 4 x^{4} (- 2 x^{2}) + 4 x^{4} \frac{1}{2} + x^{3} x^{3} + x^{3} (- 2 x^{2}) + x^{3} \frac{1}{2} - 2 x^{2} x^{3} - 2 x^{2} (- 2 x^{2}) - 2 x^{2} \frac{1}{2} + \frac{1}{4} x^{3} + \frac{1}{4} (- 2 x^{2}) + \frac{1}{4} \cdot \frac{1}{2} : x^{9} - 6 x^{8} + 12 x^{7} - \frac{13 x ^{6}}{2} - 6 x^{5} + 6 x^{4} - \frac{3 x ^{2}}{2} + \frac{3 x ^{3}}{4} + \frac{1}{8}

= x^{9} - 6 x^{8} + 12 x^{7} - \frac{13 x ^{6}}{2} - 6 x^{5} + 6 x^{4} - \frac{3 x ^{2}}{2} + \frac{3 x ^{3}}{4} + \frac{1}{8}

e x p an d A (0, - 5) y B (2.5, 0)

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

\frac{d ^{2}}{d x ^{2}} ((y) (- 2 x^{2} + 5 x))

e x p an d - \frac{14}{( x - 7 ) ^{2}}

s im pl i f y h (\frac{3 x + 5}{x + 1} + 2)