因数 m^{16}+m^8n^8+n^{16}

解

因数

m^{16} + m^{8} n^{8} + n^{16}

(m^{8} + n^{8} + m^{4} n^{4}) (m^{8} + n^{8} - m^{4} n^{4})

解答ステップ

m^{16} + m^{8} n^{8} + n^{16}

加算と減算

m^{8} n^{8}

= m^{16} + 2 m^{8} n^{8} + n^{16} - m^{8} n^{8}

因数

m^{16} + 2 m^{8} n^{8} + n^{16} : (m^{8} + n^{8})^{2}

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

指数の規則を適用する

= (m^{8} + n^{8})^{2} - (m^{4} n^{4})^{2}

因数

(m^{8} + n^{8})^{2} - (m^{4} n^{4})^{2} : (m^{8} + n^{8} + m^{4} n^{4}) (m^{8} + n^{8} - m^{4} n^{4})

= (m^{8} + n^{8} + m^{4} n^{4}) (m^{8} + n^{8} - m^{4} n^{4})