faktorisieren 27a^3-b^6

Lösung

faktorisieren

27 a^{3} - b^{6}

(3 a - b^{2}) (9 a^{2} + 3 a b^{2} + b^{4})

Schritte zur Lösung

27 a^{3} - b^{6}

Wende Exponentenregel an

= (3 a)^{3} - (b^{2})^{3}

Wende Formel zur Differenz von dritten Potenzen an:

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

(3 a)^{3} - (b^{2})^{3} = (3 a - b^{2}) ((3 a)^{2} + 3 a b^{2} + (b^{2})^{2})

= (3 a - b^{2}) ((3 a)^{2} + 3 a b^{2} + (b^{2})^{2})

Vereinfache

(3 a)^{2} + 3 a b^{2} + (b^{2})^{2} : 9 a^{2} + 3 a b^{2} + b^{4}

= (3 a - b^{2}) (9 a^{2} + 3 a b^{2} + b^{4})

x^{2} - 2 x = - 4

- 2 x^{2} + x + 4 = 0

s im pl i f y (2^{3})^{- 2}

3 (2 x + 5) + 33 \leq 0

s im pl i f y \frac{2 x ^{4} y ^{2} \cdot y x ^{- 3}}{( 2 x ^{2} y ^{2} \cdot y x ^{- 1} ) ^{- 3}}