因数 8a^3-b^6c^3

解

因数

8 a^{3} - b^{6} c^{3}

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

解答ステップ

8 a^{3} - b^{6} c^{3}

8 a^{3}

を書き換え

(2 a)^{3}

b^{6} c^{3}

を書き換え

(b^{2} c)^{3}

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

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

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

簡素化

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

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