展开 (Ae^t-Be^{-t})^2

解答

展开

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

A^{2} e^{2 t} - 2 A B + B^{2} e^{- 2 t}

求解步骤

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

使用完全平方公式:

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

a = A e^{t}, b = B e^{- t}

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

化简

(A e^{t})^{2} - 2 A e^{t} B e^{- t} + (B e^{- t})^{2} : A^{2} e^{2 t} - 2 A B + B^{2} e^{- 2 t}

= A^{2} e^{2 t} - 2 A B + B^{2} e^{- 2 t}

e x p an d A (5, - 5) Y B (8, 3)

e x p an d \frac{12 ( lo g _{2} ( 3 x - 2 ) ) ^{3}}{ln ( 2 ) ( 3 x - 2 )}

e x p an d (2 - 1)^{10}

s im pl i f y (n - \frac{m ^{2}}{n}) (\frac{n ^{2}}{m} - m)

e x p an d \frac{10}{s ( s + 2 ) ( s + 4 )}