erweitern (a^2-b^2)^3

Lösung

erweitern

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

a^{6} - 3 a^{4} b^{2} + 3 a^{2} b^{4} - b^{6}

Schritte zur Lösung

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

Wende Formel für perfekte dritte Potenzen an:

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

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

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

Vereinfache

(a^{2})^{3} - 3 (a^{2})^{2} b^{2} + 3 a^{2} (b^{2})^{2} - (b^{2})^{3} : a^{6} - 3 a^{4} b^{2} + 3 a^{2} b^{4} - b^{6}

= a^{6} - 3 a^{4} b^{2} + 3 a^{2} b^{4} - b^{6}

s im pl i f y \frac{\frac{9}{b ^{2} - b - 12}}{\frac{b - 5}{b ^{2} - b - 12}}

s im pl i f y 4^{- 2^{- 1}}

s im pl i f y 43 - 627

s im pl i f y (- 3)^{9}

s im pl i f y cos^{2} (\frac{θ}{5}) - sin^{2} (\frac{θ}{5})