展开 (1+((4sqrt(x))/(1-4x)))(sqrt(x)(1-4x))

解答

展开

(1 + (\frac{4 x}{1 - 4 x})) (x (1 - 4 x))

x - 4 x x + 4 x

求解步骤

(1 + (\frac{4 x}{1 - 4 x})) (x (1 - 4 x))

化简

1 + (\frac{4 x}{1 - 4 x}) : 1 + \frac{4 x}{1 - 4 x}

= (1 + \frac{4 x}{1 - 4 x}) x (1 - 4 x)

= x (1 + \frac{4 x}{1 - 4 x}) (1 - 4 x)

Apply FOIL method

(1 + \frac{4 x}{1 - 4 x}) (1 - 4 x) : 1 - 4 x + 4 x

= x (1 - 4 x + 4 x)

使用分配律:

m (a + b + c) = ma + mb + m c

x (1 - 4 x + 4 x) = x \cdot 1 + x (- 4 x) + x \cdot 4 x

= x \cdot 1 + x (- 4 x) + x \cdot 4 x

化简

x \cdot 1 + x (- 4 x) + x \cdot 4 x : x - 4 x x + 4 x

= x - 4 x x + 4 x

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

s im pl i f y 2 (7 - 2)

e x p an d A (3, - 4) y B (5, 1)

e x p an d ((6) (2 a e^{a x} + a^{2} e^{a x} x)) (x e^{a x})

e x p an d 1 + 2 t^{2} + 9 t 4