因数 (a-b)^3+c^6

解

因数

(a - b)^{3} + c^{6}

(a - b + c^{2}) ((a - b)^{2} - c^{2} (a - b) + c^{4})

解答ステップ

(a - b)^{3} + c^{6}

指数の規則を適用する:

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

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

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

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

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

改良

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