因数 x^8+4x^4y^4+16y^8

解

因数

x^{8} + 4 x^{4} y^{4} + 16 y^{8}

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

解答ステップ

x^{8} + 4 x^{4} y^{4} + 16 y^{8}

加算と減算

4 x^{4} y^{4}

= x^{8} + 8 x^{4} y^{4} + 16 y^{8} - 4 x^{4} y^{4}

因数

x^{8} + 8 x^{4} y^{4} + 16 y^{8} : (x^{4} + 4 y^{4})^{2}

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

指数の規則を適用する

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

因数

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

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