因数 a^3-64b^3c^3

解

因数

a^{3} - 64 b^{3} c^{3}

(a - 4 b c) (a^{2} + 4 ab c + 16 b^{2} c^{2})

解答ステップ

a^{3} - 64 b^{3} c^{3}

64 b^{3} c^{3}

を書き換え

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

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

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

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

簡素化

(a - 2^{2} b c) (a^{2} + a \cdot 2^{2} b c + (2^{2} b c)^{2}) : (a - 4 b c) (a^{2} + 4 ab c + 16 b^{2} c^{2})

= (a - 4 b c) (a^{2} + 4 ab c + 16 b^{2} c^{2})