erweitern (1-p+p*e^t)^3

Lösung

erweitern

(1 - p + p \cdot e^{t})^{3}

3 e^{t} p^{3} - 3 e^{2 t} p^{3} + e^{3 t} p^{3} - p^{3} - 6 e^{t} p^{2} + 3 e^{2 t} p^{2} + 3 p^{2} + 3 e^{t} p - 3 p + 1

Schritte zur Lösung

(1 - p + p e^{t})^{3}

= (1 - p + e^{t} p)^{3}

(1 - p + p e^{t})^{3} = (1 - p + p e^{t}) (1 - p + p e^{t}) (1 - p + p e^{t})

= (e^{t} p - p + 1) (e^{t} p - p + 1) (e^{t} p - p + 1)

Multipliziere aus

(1 - p + p e^{t}) (1 - p + p e^{t}) (1 - p + p e^{t}) : 3 e^{t} p^{3} - 3 e^{2 t} p^{3} + e^{3 t} p^{3} - p^{3} - 6 e^{t} p^{2} + 3 e^{2 t} p^{2} + 3 p^{2} + 3 e^{t} p - 3 p + 1

= 3 e^{t} p^{3} - 3 e^{2 t} p^{3} + e^{3 t} p^{3} - p^{3} - 6 e^{t} p^{2} + 3 e^{2 t} p^{2} + 3 p^{2} + 3 e^{t} p - 3 p + 1

e x p an d \frac{( 0.0224 + 2 x ) ^{2}}{( 0.00623 - x ) ( 0.00414 - x )}

e x p an d - \frac{4 ( - x + 3 ) ^{4}}{27}

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

e x p an d π (1 - x^{2})^{2}

\frac{d}{d t} ((x) (x - 2 y))