因数 x^{12}-y^{18}

解

因数

x^{12} - y^{18}

(x^{2} + y^{3}) (x^{4} - x^{2} y^{3} + y^{6}) (x^{2} - y^{3}) (x^{4} + x^{2} y^{3} + y^{6})

解答ステップ

x^{12} - y^{18}

x^{12} = (x^{6})^{2}

y^{18} = (y^{9})^{2}

= (x^{6})^{2} - (y^{9})^{2}

2乗の差の公式を適用する:

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

(x^{6})^{2} - (y^{9})^{2} = (x^{6} + y^{9}) (x^{6} - y^{9})

= (x^{6} + y^{9}) (x^{6} - y^{9})

因数

x^{6} + y^{9} : (x^{2} + y^{3}) (x^{4} - x^{2} y^{3} + y^{6})

= (x^{2} + y^{3}) (x^{4} - x^{2} y^{3} + y^{6}) (x^{6} - y^{9})

因数

x^{6} - y^{9} : (x^{2} - y^{3}) (x^{4} + x^{2} y^{3} + y^{6})

= (x^{2} + y^{3}) (x^{4} - x^{2} y^{3} + y^{6}) (x^{2} - y^{3}) (x^{4} + x^{2} y^{3} + y^{6})