因数 25m^{100}-121n^{16}

解

因数

25 m^{100} - 121 n^{16}

(5 m^{50} + 11 n^{8}) (5 m^{50} - 11 n^{8})

解答ステップ

25 m^{100} - 121 n^{16}

25 m^{100} = (5 m^{50})^{2}

121 n^{16} = (11 n^{8})^{2}

= (5 m^{50})^{2} - (11 n^{8})^{2}

2乗の差の公式を適用する:

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

(5 m^{50})^{2} - (11 n^{8})^{2} = (5 m^{50} + 11 n^{8}) (5 m^{50} - 11 n^{8})

= (5 m^{50} + 11 n^{8}) (5 m^{50} - 11 n^{8})