因数 256x^4-81y^4

解

因数

256 x^{4} - 81 y^{4}

(16 x^{2} + 9 y^{2}) (4 x + 3 y) (4 x - 3 y)

解答ステップ

256 x^{4} - 81 y^{4}

256 x^{4} = (16 x^{2})^{2}

81 y^{4} = (9 y^{2})^{2}

= (16 x^{2})^{2} - (9 y^{2})^{2}

2乗の差の公式を適用する:

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

(16 x^{2})^{2} - (9 y^{2})^{2} = (16 x^{2} + 9 y^{2}) (16 x^{2} - 9 y^{2})

= (16 x^{2} + 9 y^{2}) (16 x^{2} - 9 y^{2})

因数

16 x^{2} - 9 y^{2} : (4 x + 3 y) (4 x - 3 y)

= (16 x^{2} + 9 y^{2}) (4 x + 3 y) (4 x - 3 y)