erweitern (\sqrt[3]{x}-\sqrt[3]{c})^3

Lösung

erweitern

(3 x - 3 c)^{3}

x - 3 (3 x)^{2} 3 c + 3 (3 c)^{2} 3 x - c

Schritte zur Lösung

(3 x - 3 c)^{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 c)^{3} = (3 x)^{3} - 3 (3 x)^{2} 3 c + 3 3 x (3 c)^{2} - (3 c)^{3}

= (3 x)^{3} - 3 (3 x)^{2} 3 c + 3 3 x (3 c)^{2} - (3 c)^{3}

Vereinfache

(3 x)^{3} - 3 (3 x)^{2} 3 c + 3 3 x (3 c)^{2} - (3 c)^{3} : x - 3 (3 x)^{2} 3 c + 3 (3 c)^{2} 3 x - c

= x - 3 (3 x)^{2} 3 c + 3 (3 c)^{2} 3 x - c

e x p an d 4 (y^{4} + 3 y^{2}) + 1

e x p an d (s + 2)^{2} (s^{2} + 4 s + 4)

e x p an d \frac{1 - 2 t}{s ^{2} ( s ^{2} + s + 4 )}

e x p an d π (100 - 16 h + \frac{12 h ^{2}}{25})

s im pl i f y x (x + - x^{2} + 2) (x - - x^{2} + 2)