erweitern (2x+y^2)^3

Lösung

erweitern

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

8 x^{3} + 12 x^{2} y^{2} + 6 x y^{4} + y^{6}

Schritte zur Lösung

(2 x + 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}

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

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

Vereinfache

(2 x)^{3} + 3 (2 x)^{2} y^{2} + 3 \cdot 2 x (y^{2})^{2} + (y^{2})^{3} : 8 x^{3} + 12 x^{2} y^{2} + 6 x y^{4} + y^{6}

= 8 x^{3} + 12 x^{2} y^{2} + 6 x y^{4} + y^{6}

f a c t or x^{8} - x^{2} y^{6}

f a c t or - 75 m - m^{3} + 15 m^{2} + 125

e x p an d (4 x - x^{2}) (15 - x)

s im pl i f y 2 (3 x + 2) + 2 x

f a c t or 3 q^{2} r + 18 p^{3} q^{5} r^{5}