因数 a^3-b^{12}

解

因数

a^{3} - b^{12}

(a - b^{4}) (a^{2} + a b^{4} + b^{8})

解答ステップ

a^{3} - b^{12}

指数の規則を適用する:

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

b^{12} = (b^{4})^{3}

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

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

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

(b^{4})^{2} = b^{8}

= (a - b^{4}) (a^{2} + a b^{4} + b^{8})