因数 8x^9y^6+z^{15}

解

因数

8 x^{9} y^{6} + z^{15}

(2 x^{3} y^{2} + z^{5}) (4 x^{6} y^{4} - 2 x^{3} y^{2} z^{5} + z^{10})

解答ステップ

8 x^{9} y^{6} + z^{15}

8 x^{9} y^{6}

を書き換え

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

= (2 x^{3} y^{2})^{3} + z^{15}

指数の規則を適用する:

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

z^{15} = (z^{5})^{3}

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

立方数の和の公式を適用する:

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

(2 x^{3} y^{2})^{3} + (z^{5})^{3} = (2 x^{3} y^{2} + z^{5}) ((2 x^{3} y^{2})^{2} - 2 x^{3} y^{2} z^{5} + z^{10})

= (z^{5} + 2 x^{3} y^{2}) ((2 x^{3} y^{2})^{2} - z^{5} 2 x^{3} y^{2} + z^{10})

簡素化

(2 x^{3} y^{2} + z^{5}) ((2 x^{3} y^{2})^{2} - 2 x^{3} y^{2} z^{5} + z^{10}) : (2 x^{3} y^{2} + z^{5}) (4 x^{6} y^{4} - 2 x^{3} y^{2} z^{5} + z^{10})

= (2 x^{3} y^{2} + z^{5}) (4 x^{6} y^{4} - 2 x^{3} y^{2} z^{5} + z^{10})