因数 27a^6-(a-b)^3

解

因数

27 a^{6} - (a - b)^{3}

(3 a^{2} - a + b) (9 a^{4} + 3 a^{2} (a - b) + (a - b)^{2})

解答ステップ

27 a^{6} - (a - b)^{3}

27 a^{6} - (a - b)^{3}

を書き換え

(3 a^{2})^{3} - (a - b)^{3}

= (3 a^{2})^{3} - (a - b)^{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})

(3 a^{2})^{3} - (a - b)^{3} = (3 a^{2} - (a - b)) (3^{2} a^{4} + 3 a^{2} (a - b) + (a - b)^{2})

= (3 a^{2} - (a - b)) (3^{2} a^{4} + 3 a^{2} (a - b) + (a - b)^{2})

改良

= (3 a^{2} - a + b) (9 a^{4} + 3 a^{2} (a - b) + (a - b)^{2})