因数-169y^6+100m^2n^4

解

因数

- 169 y^{6} + 100 m^{2} n^{4}

(10 m n^{2} + 13 y^{3}) (10 m n^{2} - 13 y^{3})

解答ステップ

- 169 y^{6} + 100 m^{2} n^{4}

169 y^{6}

を書き換え

(13 y^{3})^{2}

100 m^{2} n^{4}

を書き換え

(10 m n^{2})^{2}

= - (13 y^{3})^{2} + (10 m n^{2})^{2}

2乗の差の公式を適用する:

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

(10 m n^{2})^{2} - (13 y^{3})^{2} = (10 m n^{2} + 13 y^{3}) (10 m n^{2} - 13 y^{3})

= (10 m n^{2} + 13 y^{3}) (10 m n^{2} - 13 y^{3})