展开 (e^{(-2t)}-e^{(2t)})^2

解答

展开

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

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

求解步骤

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

使用完全平方公式:

(a - b)^{2} = a^{2} - 2 ab + b^{2}

a = e^{- 2 t}, b = e^{2 t}

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

化简

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

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

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

s im pl i f y (2 + - y^{2} + y - 4)^{2}

e x p an d 16 (x - 1)^{2} + 16 (- \frac{1}{4} x + \frac{1}{4})^{2}

e x p an d (2 x^{4} - 1)^{'} \cdot (5 x^{3} - 6) + (5 x^{3} - 6)^{'} \cdot (2 x^{4} - 1)

e x p an d - K L + (U (t - \frac{e ^{x t} - 1}{x}))