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 (2, - 1) Y (- 1, - \frac{13}{7})

e x p an d \frac{x}{( 2 ln ( y ) + 1 ) y}

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

e x p an d (2 x - ux) (u d x + x d u)

e x p an d α (c, a + b + c, 4 a + 2 b + c)