因数 x^{10}-y^{10}

解

因数

x^{10} - y^{10}

(x + y) (x^{4} - x^{3} y + x^{2} y^{2} - x y^{3} + y^{4}) (x - y) (x^{4} + x^{3} y + x^{2} y^{2} + x y^{3} + y^{4})

解答ステップ

x^{10} - y^{10}

x^{10} = (x^{5})^{2}

y^{10} = (y^{5})^{2}

= (x^{5})^{2} - (y^{5})^{2}

2乗の差の公式を適用する:

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

(x^{5})^{2} - (y^{5})^{2} = (x^{5} + y^{5}) (x^{5} - y^{5})

= (x^{5} + y^{5}) (x^{5} - y^{5})

因数

x^{5} + y^{5} : (x + y) (x^{4} - x^{3} y + x^{2} y^{2} - x y^{3} + y^{4})

= (x + y) (x^{4} - x^{3} y + x^{2} y^{2} - x y^{3} + y^{4}) (x^{5} - y^{5})

因数

x^{5} - y^{5} : (x - y) (x^{4} + x^{3} y + x^{2} y^{2} + x y^{3} + y^{4})

= (x + y) (x^{4} - x^{3} y + x^{2} y^{2} - x y^{3} + y^{4}) (x - y) (x^{4} + x^{3} y + x^{2} y^{2} + x y^{3} + y^{4})