展开 (t^2-1)(t^2-2t)e^{(t^2+1)(t^2-2t)}

解答

展开

(t^{2} - 1) (t^{2} - 2 t) e^{(t^{2} + 1) (t^{2} - 2 t)}

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

求解步骤

(t^{2} - 1) (t^{2} - 2 t) e^{(t^{2} + 1) (t^{2} - 2 t)}

= e^{(t^{2} + 1) (t^{2} - 2 t)} (t^{2} - 1) (t^{2} - 2 t)

乘开

(t^{2} - 1) (t^{2} - 2 t) : t^{4} - 2 t^{3} - t^{2} + 2 t

= e^{(t^{2} + 1) (t^{2} - 2 t)} (t^{4} - 2 t^{3} - t^{2} + 2 t)

乘开

e^{(t^{2} + 1) (t^{2} - 2 t)} (t^{4} - 2 t^{3} - t^{2} + 2 t) : e^{t^{4} - 2 t^{3} + t^{2} - 2 t} t^{4} - 2 e^{t^{4} - 2 t^{3} + t^{2} - 2 t} t^{3} - e^{t^{4} - 2 t^{3} + t^{2} - 2 t} t^{2} + 2 e^{t^{4} - 2 t^{3} + t^{2} - 2 t} t

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

e x p an d 4 (π + 8)

e x p an d \frac{6}{x ( x - 3 )}

e x p an d \frac{a}{s ^{2} ( s ^{2} + b )}

e x p an d (cos (x) + i sin (x))^{4}

\frac{\partial}{\partial x} ((z) (x^{2} + x y^{2} z))