因数 64a^3b^6c^9-1

解

因数

64 a^{3} b^{6} c^{9} - 1

(4 a b^{2} c^{3} - 1) (16 a^{2} b^{4} c^{6} + 4 a b^{2} c^{3} + 1)

解答ステップ

64 a^{3} b^{6} c^{9} - 1

64 a^{3} b^{6} c^{9}

を書き換え

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

= (2^{2} a b^{2} c^{3})^{3} - 1

1

を書き換え

1^{3}

= (2^{2} a b^{2} c^{3})^{3} - 1^{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^{2} a b^{2} c^{3})^{3} - 1^{3} = (2^{2} a b^{2} c^{3} - 1) ((2^{2} a b^{2} c^{3})^{2} + 2^{2} a b^{2} c^{3} + 1)

= (2^{2} a b^{2} c^{3} - 1) ((2^{2} a b^{2} c^{3})^{2} + 2^{2} a b^{2} c^{3} + 1)

簡素化

(2^{2} a b^{2} c^{3} - 1) ((2^{2} a b^{2} c^{3})^{2} + 2^{2} a b^{2} c^{3} + 1) : (4 a b^{2} c^{3} - 1) (16 a^{2} b^{4} c^{6} + 4 a b^{2} c^{3} + 1)

= (4 a b^{2} c^{3} - 1) (16 a^{2} b^{4} c^{6} + 4 a b^{2} c^{3} + 1)