faktorisieren x^3+1/8

Lösung

faktorisieren

x^{3} + \frac{1}{8}

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

Schritte zur Lösung

x^{3} + \frac{1}{8}

Wende Radikal Regel an:

a = (a)^{2}

\frac{1}{8} = (3 \frac{1}{8})^{3}

= x^{3} + (3 \frac{1}{8})^{3}

Wende Formel zur Summe von dritten Potenzen an:

x^{3} + y^{3} = (x + y) (x^{2} - x y + y^{2})

x^{3} + (3 \frac{1}{8})^{3} = (x + \frac{1}{2}) (x^{2} - \frac{x}{2} + (\frac{1}{2})^{2})

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

Vereinfache

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

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

s im pl i f y (x + h) (x + h)

\frac{2 m ^{2} + 16}{5} = 2 m

s im pl i f y - 8 - 11

x^{2} + 60 = 16 x

x^{2} - 8 x = 0