erweitern 2t^2e^{kt}(2e^{kt}-y)

Lösung

erweitern

2 t^{2} e^{k t} (2 e^{k t} - y)

4 e^{2 t k} t^{2} - 2 e^{t k} t^{2} y

Schritte zur Lösung

2 t^{2} e^{k t} (2 e^{k t} - y)

= 2 e^{t k} t^{2} (2 e^{t k} - y)

Wende das Distributivgesetz an:

a (b - c) = ab - a c

a = 2 t^{2} e^{k t}, b = 2 e^{k t}, c = y

= 2 t^{2} e^{k t} \cdot 2 e^{k t} - 2 t^{2} e^{k t} y

= 2 \cdot 2 e^{t k} e^{t k} t^{2} - 2 e^{t k} t^{2} y

2 \cdot 2 e^{t k} e^{t k} t^{2} = 4 e^{2 t k} t^{2}

= 4 e^{2 t k} t^{2} - 2 e^{t k} t^{2} y

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

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

\frac{d ^{4}}{d x ^{4}} ((y) (cos (x) + 2))

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

e x p an d (- (\frac{3 x}{4} + 3) cos (\frac{3 x}{4} + 3)) + sin (\frac{3 x}{4} + 3)