erweitern (5x^3+2y^2)^3

Lösung

erweitern

(5 x^{3} + 2 y^{2})^{3}

125 x^{9} + 150 x^{6} y^{2} + 60 x^{3} y^{4} + 8 y^{6}

Schritte zur Lösung

(5 x^{3} + 2 y^{2})^{3}

Wende Formel für perfekte dritte Potenzen an:

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

(5 x^{3} + 2 y^{2})^{3} = (5 x^{3})^{3} + 3 (5 x^{3})^{2} \cdot 2 y^{2} + 3 \cdot 5 x^{3} (2 y^{2})^{2} + (2 y^{2})^{3}

= (5 x^{3})^{3} + 3 (5 x^{3})^{2} \cdot 2 y^{2} + 3 \cdot 5 x^{3} (2 y^{2})^{2} + (2 y^{2})^{3}

Vereinfache

(5 x^{3})^{3} + 3 (5 x^{3})^{2} \cdot 2 y^{2} + 3 \cdot 5 x^{3} (2 y^{2})^{2} + (2 y^{2})^{3} : 125 x^{9} + 150 x^{6} y^{2} + 60 x^{3} y^{4} + 8 y^{6}

= 125 x^{9} + 150 x^{6} y^{2} + 60 x^{3} y^{4} + 8 y^{6}

s im pl i f y x^{6} y^{4} \cdot x y

f a c t or 3 x^{4} - 24 x

f a c t or + 75 a^{2} c - 45 a^{2} d - 30 b c + 18 b d

e x p an d (a - b)^{2} - c^{2}

s im pl i f y \frac{1}{2 x} + \frac{8}{9 y}