因数 125a^9b^3+64c^3d^6

解

因数

125 a^{9} b^{3} + 64 c^{3} d^{6}

(5 a^{3} b + 4 c d^{2}) (25 a^{6} b^{2} - 20 a^{3} b c d^{2} + 16 c^{2} d^{4})

解答ステップ

125 a^{9} b^{3} + 64 c^{3} d^{6}

125 a^{9} b^{3}

を書き換え

(5 a^{3} b)^{3}

64 c^{3} d^{6}

を書き換え

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

= (5 a^{3} b)^{3} + (2^{2} c d^{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})

(5 a^{3} b)^{3} + (2^{2} c d^{2})^{3} = (5 a^{3} b + 2^{2} c d^{2}) ((5 a^{3} b)^{2} - 2^{2} c d^{2} 5 a^{3} b + (2^{2} c d^{2})^{2})

= (2^{2} c d^{2} + 5 a^{3} b) ((2^{2} c d^{2})^{2} - 2^{2} c d^{2} 5 a^{3} b + (5 a^{3} b)^{2})

簡素化

(5 a^{3} b + 2^{2} c d^{2}) ((5 a^{3} b)^{2} - 2^{2} c d^{2} \cdot 5 a^{3} b + (2^{2} c d^{2})^{2}) : (5 a^{3} b + 4 c d^{2}) (25 a^{6} b^{2} - 20 a^{3} b c d^{2} + 16 c^{2} d^{4})

= (5 a^{3} b + 4 c d^{2}) (25 a^{6} b^{2} - 20 a^{3} b c d^{2} + 16 c^{2} d^{4})