erweitern (5m^2+2n^5)^3

Lösung

erweitern

(5 m^{2} + 2 n^{5})^{3}

125 m^{6} + 150 m^{4} n^{5} + 60 m^{2} n^{10} + 8 n^{15}

Schritte zur Lösung

(5 m^{2} + 2 n^{5})^{3}

Wende Formel für perfekte dritte Potenzen an:

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

(5 m^{2} + 2 n^{5})^{3} = (5 m^{2})^{3} + 3 (5 m^{2})^{2} \cdot 2 n^{5} + 3 \cdot 5 m^{2} (2 n^{5})^{2} + (2 n^{5})^{3}

= (5 m^{2})^{3} + 3 (5 m^{2})^{2} \cdot 2 n^{5} + 3 \cdot 5 m^{2} (2 n^{5})^{2} + (2 n^{5})^{3}

Vereinfache

(5 m^{2})^{3} + 3 (5 m^{2})^{2} \cdot 2 n^{5} + 3 \cdot 5 m^{2} (2 n^{5})^{2} + (2 n^{5})^{3} : 125 m^{6} + 150 m^{4} n^{5} + 60 m^{2} n^{10} + 8 n^{15}

= 125 m^{6} + 150 m^{4} n^{5} + 60 m^{2} n^{10} + 8 n^{15}

s im pl i f y \frac{1}{3} - \frac{2}{9}

f a c t or x^{6} - 36

\frac{100}{12}

e x p an d (s - 1) (s + 1)

s im pl i f y \frac{1}{5} a x + \frac{3}{10} a x + a x