展开 (e^x-5)^3

解答

展开

(e^{x} - 5)^{3}

e^{3 x} - 15 e^{2 x} + 75 e^{x} - 125

求解步骤

(e^{x} - 5)^{3}

使用完全立方公式:

(a - b)^{3} = a^{3} - 3 a^{2} b + 3 a b^{2} - b^{3}

a = e^{x}, b = 5

= (e^{x})^{3} - 3 (e^{x})^{2} \cdot 5 + 3 e^{x} \cdot 5^{2} - 5^{3}

化简

(e^{x})^{3} - 3 (e^{x})^{2} \cdot 5 + 3 e^{x} \cdot 5^{2} - 5^{3} : e^{3 x} - 15 e^{2 x} + 75 e^{x} - 125

= e^{3 x} - 15 e^{2 x} + 75 e^{x} - 125

e x p an d \frac{9 x ( 2 x + 5 )}{( 5 x - 2 ) ^{2}}

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

e x p an d \frac{4 n}{( 2 + 2 i ) ^{2}}

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

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