簡約 (2xsqrt(x^2+1))^2

解

簡約

(2 x x^{2} + 1)^{2}

4 x^{2} (x^{2} + 1)

解答ステップ

(2 x x^{2} + 1)^{2}

指数の規則を適用する:

(a \cdot b)^{n} = a^{n} b^{n}

(2 x x^{2} + 1)^{2} = 2^{2} x^{2} (x^{2} + 1)^{2}

= 2^{2} x^{2} (x^{2} + 1)^{2}

2^{2} = 4

= 4 x^{2} (x^{2} + 1)^{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

(x^{2} + 1)^{2} = x^{2} + 1

= 4 x^{2} (x^{2} + 1)