因数 a^{10}+x^{10}

解

因数

a^{10} + x^{10}

(a^{2} + x^{2}) (a^{8} + x^{8} - x^{2} a^{6} + x^{4} a^{4} - x^{6} a^{2})

解答ステップ

a^{10} + x^{10}

指数の規則を適用する

= (a^{2})^{5} + (x^{2})^{5}

因数分解の規則を適用する:

x^{n} + y^{n} = (x + y) (x^{n - 1} - x^{n - 2} y + \dots - x y^{n - 2} + y^{n - 1}), n i s o dd

(a^{2})^{5} + (x^{2})^{5} = (a^{2} + x^{2}) (a^{8} - x^{2} a^{6} + x^{4} a^{4} - x^{6} a^{2} + x^{8})

= (a^{2} + x^{2}) (a^{8} - x^{2} a^{6} + x^{4} a^{4} - x^{6} a^{2} + x^{8})

= (a^{2} + x^{2}) (a^{8} + x^{8} - x^{2} a^{6} + x^{4} a^{4} - x^{6} a^{2})