展开 (e^x-1)(e^x-x)^2

解答

展开

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

e^{3 x} - 2 e^{2 x} x + e^{x} x^{2} - e^{2 x} + 2 e^{x} x - x^{2}

求解步骤

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

使用分配律:

a (b - c) = ab - a c

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

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

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

化简

e^{x} (e^{x} - x)^{2} - 1 \cdot (e^{x} - x)^{2} : e^{3 x} - 2 e^{2 x} x + e^{x} x^{2} - e^{2 x} + 2 e^{x} x - x^{2}

= e^{3 x} - 2 e^{2 x} x + e^{x} x^{2} - e^{2 x} + 2 e^{x} x - x^{2}

e x p an d (2 x^{2} + 3 x - 3) e^{x}

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

e x p an d \frac{k - 5}{k ( 5 k + 1 )}

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

e x p an d (1 + x + x^{2})^{9}