展开 (1-ce^{-(x^2)/2})^2

解答

展开

(1 - c e^{- \frac{x ^{2}}{2}})^{2}

1 - 2 c e^{- \frac{x ^{2}}{2}} + c^{2} e^{- x^{2}}

求解步骤

(1 - c e^{- \frac{x ^{2}}{2}})^{2}

使用完全平方公式:

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

a = 1, b = c e^{- \frac{x ^{2}}{2}}

= 1^{2} - 2 \cdot 1 \cdot c e^{- \frac{x ^{2}}{2}} + (c e^{- \frac{x ^{2}}{2}})^{2}

化简

1^{2} - 2 \cdot 1 \cdot c e^{- \frac{x ^{2}}{2}} + (c e^{- \frac{x ^{2}}{2}})^{2} : 1 - 2 c e^{- \frac{x ^{2}}{2}} + c^{2} e^{- x^{2}}

= 1 - 2 c e^{- \frac{x ^{2}}{2}} + c^{2} e^{- x^{2}}

e x p an d \frac{( 1 + r ) ( 1 - a ) ( x ) + c}{( 1 + r )}

e x p an d 2 x^{2} - x^{- 1}

e x p an d y^{2} (e^{x y} + e^{x y} x y)

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

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