erweitern (a-3b^2)^3

Lösung

erweitern

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

a^{3} - 9 a^{2} b^{2} + 27 a b^{4} - 27 b^{6}

Schritte zur Lösung

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

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

Vereinfache

a^{3} - 3 a^{2} \cdot 3 b^{2} + 3 a (3 b^{2})^{2} - (3 b^{2})^{3} : a^{3} - 9 a^{2} b^{2} + 27 a b^{4} - 27 b^{6}

= a^{3} - 9 a^{2} b^{2} + 27 a b^{4} - 27 b^{6}

s im pl i f y (5 y^{2})^{2}

f a c t or 2 x^{4} - 2 y^{2} + 2 x^{2} y^{2} - 2

e x p an d (p + 2) (p - 8)

s im pl i f y 4 n^{2} + (3 n)^{2}

s im pl i f y 3 a (a - 1) + 1 - (2 a - a)