erweitern (\sqrt[3]{4}-\sqrt[3]{x})^3

Lösung

erweitern

(34 - 3 x)^{3}

4 - 3 (34)^{2} 3 x + 334 (3 x)^{2} - x

Schritte zur Lösung

(34 - 3 x)^{3}

Wende Formel für perfekte dritte Potenzen an:

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

(34 - 3 x)^{3} = (34)^{3} - 3 (34)^{2} 3 x + 334 (3 x)^{2} - (3 x)^{3}

= (34)^{3} - 3 (34)^{2} 3 x + 334 (3 x)^{2} - (3 x)^{3}

Vereinfache

(34)^{3} - 3 (34)^{2} 3 x + 334 (3 x)^{2} - (3 x)^{3} : 4 - 3 (34)^{2} 3 x + 334 (3 x)^{2} - x

= 4 - 3 (34)^{2} 3 x + 334 (3 x)^{2} - x

e x p an d \frac{( x + 1 ) ^{5}}{x ^{6} + 2 x ^{4} + x ^{2}}

e x p an d \frac{33 x ^{2} + 9 x + 1}{( 3 - x ) ( 7 x ^{2} + 2 )}

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

e x p an d \frac{x ( x + 2 )}{( x - 3 ) ( x - 2 )}

e x p an d \frac{10 ( x - 4 )}{3}