erweitern (\sqrt[3]{A}+\sqrt[3]{B})^3

Lösung

erweitern

(3 A + 3 B)^{3}

A + 3 (3 A)^{2} 3 B + 3 (3 B)^{2} 3 A + B

Schritte zur Lösung

(3 A + 3 B)^{3}

Wende Formel für perfekte dritte Potenzen an:

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

(3 A + 3 B)^{3} = (3 A)^{3} + 3 (3 A)^{2} 3 B + 3 3 A (3 B)^{2} + (3 B)^{3}

= (3 A)^{3} + 3 (3 A)^{2} 3 B + 3 3 A (3 B)^{2} + (3 B)^{3}

Vereinfache

(3 A)^{3} + 3 (3 A)^{2} 3 B + 3 3 A (3 B)^{2} + (3 B)^{3} : A + 3 (3 A)^{2} 3 B + 3 (3 B)^{2} 3 A + B

= A + 3 (3 A)^{2} 3 B + 3 (3 B)^{2} 3 A + B

e x p an d 3 e^{- \frac{x}{5}} (x + 5) + 1

e x p an d \frac{( 6 x ^{2} - 9 x + 1 )}{( x - 1 ) ^{2} ( x + 1 )}

e x p an d (ln (2 x + 6) + \frac{x}{x + 3}) (2 x + 6)^{x}

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

e x p an d 2 (y (z - 2))