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}

s im pl i f y (x - 3) (x + 2) (x + 3) (x + 8) + 56

s im pl i f y \frac{5}{sin ^{2} ( a )} - 5 cot^{2} (a)

s im pl i f y \frac{a}{2} + \frac{a ^{3}}{2} + \frac{a ^{5}}{2}

f a c t or a^{3} b^{2} + a^{2} b^{3}

f a c t or y^{5} - y^{3} - y^{2} + 1