展开 (3x+2e)^3

解答

展开

(3 x + 2 e)^{3}

27 x^{3} + 54 e x^{2} + 36 e^{2} x + 8 e^{3}

求解步骤

(3 x + 2 e)^{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 = 3 x, b = 2 e

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

化简

(3 x)^{3} + 3 (3 x)^{2} \cdot 2 e + 3 \cdot 3 x (2 e)^{2} + (2 e)^{3} : 27 x^{3} + 54 e x^{2} + 36 e^{2} x + 8 e^{3}

= 27 x^{3} + 54 e x^{2} + 36 e^{2} x + 8 e^{3}

e x p an d - e^{\frac{y x}{2}} csc^{2} (e^{\frac{y x}{2}}) (z x + y)

s im pl i f y (x y + \frac{5}{8}) (\frac{3}{4} - x y)

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

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

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