因数-400x^4y^4+9z^6

解

因数

- 400 x^{4} y^{4} + 9 z^{6}

(3 z^{3} + 20 x^{2} y^{2}) (3 z^{3} - 20 x^{2} y^{2})

解答ステップ

- 400 x^{4} y^{4} + 9 z^{6}

400 x^{4} y^{4}

を書き換え

(20 x^{2} y^{2})^{2}

9 z^{6}

を書き換え

(3 z^{3})^{2}

= - (20 x^{2} y^{2})^{2} + (3 z^{3})^{2}

2乗の差の公式を適用する:

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

(3 z^{3})^{2} - (20 x^{2} y^{2})^{2} = (3 z^{3} + 20 x^{2} y^{2}) (3 z^{3} - 20 x^{2} y^{2})

= (3 z^{3} + 20 x^{2} y^{2}) (3 z^{3} - 20 x^{2} y^{2})