展开 (x-1)^2(e^x-1)

解答

展开

(x - 1)^{2} (e^{x} - 1)

e^{x} x^{2} - 2 e^{x} x + e^{x} - x^{2} + 2 x - 1

求解步骤

(x - 1)^{2} (e^{x} - 1)

使用分配律:

a (b - c) = ab - a c

a = (x - 1)^{2}, b = e^{x}, c = 1

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

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

化简

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

= e^{x} x^{2} - 2 e^{x} x + e^{x} - x^{2} + 2 x - 1

e x p an d \frac{- 4 s - 11}{( s + 2 ) ^{2}}

e x p an d ln (5) (5 - x^{4})

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

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

e x p an d (3125 π + 31132374) m