因数 81x^4-16y^4

解

因数

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

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

解答ステップ

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

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

16 y^{4} = (4 y^{2})^{2}

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

2乗の差の公式を適用する:

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

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

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

因数

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

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