展开 (b-x+sqrt(((x+b)(5b-3*x))))^2

解答

展开

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

6 b^{2} - 2 x^{2} + 2 b - 3 x^{2} + 2 b x + 5 b^{2} - 2 x - 3 x^{2} + 2 b x + 5 b^{2}

求解步骤

(b - x + (x + b) (5 b - 3 x))^{2}

化简

b - x + (x + b) (5 b - 3 x) : b - x + (x + b) (5 b - 3 x)

= (b - x + (x + b) (5 b - 3 x))^{2}

使用指数法则:

a^{b + c} = a^{b} \cdot a^{c}

(b - x + (x + b) (5 b - 3 x))^{2} = (b - x + (x + b) (5 b - 3 x)) (b - x + (x + b) (5 b - 3 x))

= (b - x + (x + b) (5 b - 3 x)) (b - x + (x + b) (5 b - 3 x))

打开括号

= bb + b (- x) + b (x + b) (5 b - 3 x) - x b - x (- x) - x (x + b) (5 b - 3 x) + (x + b) (5 b - 3 x) b + (x + b) (5 b - 3 x) (- x) + (x + b) (5 b - 3 x) (x + b) (5 b - 3 x)

化简

bb + b (- x) + b (x + b) (5 b - 3 x) - x b - x (- x) - x (x + b) (5 b - 3 x) + (x + b) (5 b - 3 x) b + (x + b) (5 b - 3 x) (- x) + (x + b) (5 b - 3 x) (x + b) (5 b - 3 x) : 6 b^{2} - 2 x^{2} + 2 b - 3 x^{2} + 2 b x + 5 b^{2} - 2 x - 3 x^{2} + 2 b x + 5 b^{2}

= 6 b^{2} - 2 x^{2} + 2 b - 3 x^{2} + 2 b x + 5 b^{2} - 2 x - 3 x^{2} + 2 b x + 5 b^{2}

s im pl i f y (x - 2) (x + 6) (x - \frac{1}{2})

s im pl i f y (cos (t) \cdot t + 2 sin (t)) \cdot (cos (t))

e x p an d u (\frac{v - u}{a})

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

e x p an d π (19.44923 - x)^{2}