展開する (b-x+sqrt(((x+b)(5b-3*x))))^2

解

展開する

(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}

解答ステップ

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

簡素化

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}

指数の規則を適用する:

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))

括弧を分配する

= 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)

簡素化

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}