簡約 (sqrt(2x-\sqrt{4x-3)})^4

解

簡約

(2 x - 4 x - 3)^{4}

4 x^{2} - 4 x 4 x - 3 + 4 x - 3

解答ステップ

(2 x - 4 x - 3)^{4}

4

を書き換え

2 \cdot 2

= (2 x - 4 x - 3)^{2 \cdot 2}

指数の規則を適用する:

a^{b c} = (a^{b})^{c},

, 以下を想定

a \geq 0

(2 x - 4 x - 3)^{2 \cdot 2} = ((2 x - 4 x - 3)^{2})^{2}

= ((2 x - 4 x - 3)^{2})^{2}

指数の規則を適用する:

(n a)^{n} = a,

, 以下を想定

n i s o dd or a \geq 0

(2 x - 4 x - 3)^{2} = 2 x - 4 x - 3

= (2 x - 4 x - 3)^{2}

完全平方式を適用する:

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

(2 x - 4 x - 3)^{2} = (2 x)^{2} - 2 \cdot 2 x 4 x - 3 + (4 x - 3)^{2}

= (2 x)^{2} - 2 \cdot 2 x 4 x - 3 + (4 x - 3)^{2}

(2 x)^{2} = 4 x^{2}

- 2 \cdot 2 x 4 x - 3 = - 4 x 4 x - 3

(4 x - 3)^{2} = 4 x - 3

= 4 x^{2} - 4 x 4 x - 3 + 4 x - 3