因数 x^3-y^6

解

因数

x^{3} - y^{6}

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

解答ステップ

x^{3} - y^{6}

指数の規則を適用する:

a^{b c} = (a^{b})^{c}

y^{6} = (y^{2})^{3}

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

立方数の差の公式を適用する:

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

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

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

(y^{2})^{2} = y^{4}

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