erweitern (3m-2n^2)^3

Lösung

erweitern

(3 m - 2 n^{2})^{3}

27 m^{3} - 54 m^{2} n^{2} + 36 m n^{4} - 8 n^{6}

Schritte zur Lösung

(3 m - 2 n^{2})^{3}

Wende Formel für perfekte dritte Potenzen an:

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

(3 m - 2 n^{2})^{3} = (3 m)^{3} - 3 (3 m)^{2} \cdot 2 n^{2} + 3 \cdot 3 m (2 n^{2})^{2} - (2 n^{2})^{3}

= (3 m)^{3} - 3 (3 m)^{2} \cdot 2 n^{2} + 3 \cdot 3 m (2 n^{2})^{2} - (2 n^{2})^{3}

Vereinfache

(3 m)^{3} - 3 (3 m)^{2} \cdot 2 n^{2} + 3 \cdot 3 m (2 n^{2})^{2} - (2 n^{2})^{3} : 27 m^{3} - 54 m^{2} n^{2} + 36 m n^{4} - 8 n^{6}

= 27 m^{3} - 54 m^{2} n^{2} + 36 m n^{4} - 8 n^{6}

s im pl i f y 2 cos (x) \cdot sin (x)

s im pl i f y (\frac{1 + i}{1 - i})^{8}

e x p an d (a^{3} + b^{3})^{2}

\frac{46}{7}

f a c t or 6 m^{2} - 25 m - 9