因数 9-4x^4y^6

解

因数

9 - 4 x^{4} y^{6}

(3 + 2 x^{2} y^{3}) (3 - 2 x^{2} y^{3})

解答ステップ

9 - 4 x^{4} y^{6}

9 = 3^{2}

4 x^{4} y^{6} = (2 x^{2} y^{3})^{2}

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

2乗の差の公式を適用する:

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

3^{2} - (2 x^{2} y^{3})^{2} = (3 + 2 x^{2} y^{3}) (3 - 2 x^{2} y^{3})

= (3 + 2 x^{2} y^{3}) (3 - 2 x^{2} y^{3})