erweitern (3x^3y-2z^4)^3

Lösung

erweitern

(3 x^{3} y - 2 z^{4})^{3}

27 x^{9} y^{3} - 54 x^{6} y^{2} z^{4} + 36 x^{3} y z^{8} - 8 z^{12}

Schritte zur Lösung

(3 x^{3} y - 2 z^{4})^{3}

Wende Formel für perfekte dritte Potenzen an:

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

(3 x^{3} y - 2 z^{4})^{3} = (3 x^{3} y)^{3} - 3 (3 x^{3} y)^{2} \cdot 2 z^{4} + 3 \cdot 3 x^{3} y (2 z^{4})^{2} - (2 z^{4})^{3}

= (3 x^{3} y)^{3} - 3 (3 x^{3} y)^{2} \cdot 2 z^{4} + 3 \cdot 3 x^{3} y (2 z^{4})^{2} - (2 z^{4})^{3}

Vereinfache

(3 x^{3} y)^{3} - 3 (3 x^{3} y)^{2} \cdot 2 z^{4} + 3 \cdot 3 x^{3} y (2 z^{4})^{2} - (2 z^{4})^{3} : 27 x^{9} y^{3} - 54 x^{6} y^{2} z^{4} + 36 x^{3} y z^{8} - 8 z^{12}

= 27 x^{9} y^{3} - 54 x^{6} y^{2} z^{4} + 36 x^{3} y z^{8} - 8 z^{12}

e x p an d (x + 2) (x + 8)

e x p an d (x + 2) (x + 9)

s im pl i f y 10 - 5 (9 n - 9)

s im pl i f y 2 tan (θ) (3 cos (θ))

e x p an d (x - 1) (x + 1) (x - 2)