因数 x^4+3x^2y^2+4y^4

解

因数

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

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

解答ステップ

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

加算と減算

x^{2} y^{2}

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

因数

x^{4} + 4 x^{2} y^{2} + 4 y^{4} : (x^{2} + 2 y^{2})^{2}

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

指数の規則を適用する:

a^{m} b^{m} = (ab)^{m}

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

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

因数

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

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