erweitern (3sqrt(3)a-sqrt(3)x)^3

Lösung

erweitern

(33 a - 3 x)^{3}

813 a^{3} - 813 x a^{2} + 273 a x^{2} - 33 x^{3}

Schritte zur Lösung

(33 a - 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}

(33 a - 3 x)^{3} = (33 a)^{3} - 3 (33 a)^{2} 3 x + 3 \cdot 33 a (3 x)^{2} - (3 x)^{3}

= (33 a)^{3} - 3 (33 a)^{2} 3 x + 3 \cdot 33 a (3 x)^{2} - (3 x)^{3}

Vereinfache

(33 a)^{3} - 3 (33 a)^{2} 3 x + 3 \cdot 33 a (3 x)^{2} - (3 x)^{3} : 813 a^{3} - 813 x a^{2} + 273 a x^{2} - 33 x^{3}

= 813 a^{3} - 813 x a^{2} + 273 a x^{2} - 33 x^{3}

e x p an d \frac{( 1 - 4 x ^{3} ) ( 3 + 8 x ^{3} )}{( 8 x ^{2} - 1 ) ( 8 x ^{2} - 3 )}

s im pl i f y (x - 1 + 6) (x - 1 - 6) (x + 2 - 42)

e x p an d \frac{4}{( x + 2 ) ^{3}}

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

e x p an d - 4 (x - 2) e^{8 x}