erweitern (2+2te-3t^2+4t^3)u_{2}(t)

Lösung

erweitern

(2 + 2 t e - 3 t^{2} + 4 t^{3}) u_{2} (t)

2 t u_{2} + 2 e t^{2} u_{2} - 3 t^{3} u_{2} + 4 t^{4} u_{2}

Schritte zur Lösung

(2 + 2 t e - 3 t^{2} + 4 t^{3}) u_{2} (t)

= (t) u_{2} (2 + 2 e t - 3 t^{2} + 4 t^{3})

Setze Klammern

= u_{2} (t) \cdot 2 + u_{2} (t) \cdot 2 t e + u_{2} (t) (- 3 t^{2}) + u_{2} (t) \cdot 4 t^{3}

Wende Minus-Plus Regeln an

+ (- a) = - a

= 2 (t) u_{2} + 2 e (t) t u_{2} - 3 t^{2} (t) u_{2} + 4 t^{3} (t) u_{2}

Vereinfache

2 (t) u_{2} + 2 e (t) t u_{2} - 3 t^{2} (t) u_{2} + 4 t^{3} (t) u_{2} : 2 t u_{2} + 2 e t^{2} u_{2} - 3 t^{3} u_{2} + 4 t^{4} u_{2}

= 2 t u_{2} + 2 e t^{2} u_{2} - 3 t^{3} u_{2} + 4 t^{4} u_{2}

e x p an d \frac{12}{( x + 2 ) ( x - 2 )}

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

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

e x p an d (e - 3)^{2}

e x p an d \frac{2}{729} (- 9 e^{- 9 x} x - e^{- 9 x})