因数 16x^8-81y^4

解

因数

16 x^{8} - 81 y^{4}

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

解答ステップ

16 x^{8} - 81 y^{4}

16 x^{8} = (4 x^{4})^{2}

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

= (4 x^{4})^{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)

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

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

因数

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

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