因数 x^6+x^3-y^6-y^3

解

因数

x^{6} + x^{3} - y^{6} - y^{3}

(x - y) (x^{2} + x y + y^{2}) (x^{3} + y^{3} + 1)

解答ステップ

x^{6} + x^{3} - y^{6} - y^{3}

因数

x^{6} - y^{6} : (x + y) (x^{2} - x y + y^{2}) (x - y) (x^{2} + x y + y^{2})

因数

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

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

共通項をくくり出す

(x - y) (x^{2} + x y + y^{2}) : (x - y) (x^{2} + x y + y^{2}) ((x + y) (x^{2} - x y + y^{2}) + 1)

= (x - y) (x^{2} + x y + y^{2}) ((x + y) (x^{2} - x y + y^{2}) + 1)

拡張

(x + y) (x^{2} - x y + y^{2}) + 1 : x^{3} + y^{3} + 1

= (x - y) (x^{2} + x y + y^{2}) (x^{3} + y^{3} + 1)