簡約 (xsqrt(y^2+1)+ysqrt(x^2+1))^2

解

簡約

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

2 x^{2} y^{2} + x^{2} + 2 x y y^{2} + 1 x^{2} + 1 + y^{2}

解答ステップ

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

完全平方式を適用する:

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

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

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

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

2 x y^{2} + 1 y x^{2} + 1 = 2 x y y^{2} + 1 x^{2} + 1

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

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

簡素化

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

= 2 x^{2} y^{2} + x^{2} + 2 x y y^{2} + 1 x^{2} + 1 + y^{2}