erweitern (3x+3z^2)^3

Lösung

erweitern

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

27 x^{3} + 81 x^{2} z^{2} + 81 x z^{4} + 27 z^{6}

Schritte zur Lösung

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

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

Vereinfache

(3 x)^{3} + 3 (3 x)^{2} \cdot 3 z^{2} + 3 \cdot 3 x (3 z^{2})^{2} + (3 z^{2})^{3} : 27 x^{3} + 81 x^{2} z^{2} + 81 x z^{4} + 27 z^{6}

= 27 x^{3} + 81 x^{2} z^{2} + 81 x z^{4} + 27 z^{6}

s im pl i f y 2 4^{0}

e x p an d x^{2} (- 2 x^{2} - x - 10)

s im pl i f y \frac{6}{16} + \frac{3}{128}

s im pl i f y \frac{3}{16} + \frac{4}{128}

e x p an d (7 x - 3) (x^{2} - 2 x + 7)