erweitern (3ay+Ce^{6x})^3

Lösung

erweitern

(3 a y + C e^{6 x})^{3}

27 a^{3} y^{3} + 27 a^{2} C e^{6 x} y^{2} + 9 a C^{2} e^{12 x} y + C^{3} e^{18 x}

Schritte zur Lösung

(3 a y + C e^{6 x})^{3}

Wende Formel für perfekte dritte Potenzen an:

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

a = 3 a y, b = C e^{6 x}

= (3 a y)^{3} + 3 (3 a y)^{2} C e^{6 x} + 3 \cdot 3 a y (C e^{6 x})^{2} + (C e^{6 x})^{3}

Vereinfache

(3 a y)^{3} + 3 (3 a y)^{2} C e^{6 x} + 3 \cdot 3 a y (C e^{6 x})^{2} + (C e^{6 x})^{3} : 27 a^{3} y^{3} + 27 a^{2} C e^{6 x} y^{2} + 9 a C^{2} e^{12 x} y + C^{3} e^{18 x}

= 27 a^{3} y^{3} + 27 a^{2} C e^{6 x} y^{2} + 9 a C^{2} e^{12 x} y + C^{3} e^{18 x}

e x p an d \frac{x y}{x ^{2}}

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

e x p an d d y (3 x^{2} + 5 = y)

e x p an d (2 + sin (e^{- b x} + 1))^{2}

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