因数 b^6c^9+d^3

解

因数

b^{6} c^{9} + d^{3}

(b^{2} c^{3} + d) (b^{4} c^{6} - b^{2} c^{3} d + d^{2})

解答ステップ

b^{6} c^{9} + d^{3}

b^{6} c^{9}

を書き換え

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

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

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

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

簡素化

(b^{2} c^{3} + d) ((b^{2} c^{3})^{2} - b^{2} c^{3} d + d^{2}) : (b^{2} c^{3} + d) (b^{4} c^{6} - b^{2} c^{3} d + d^{2})

= (b^{2} c^{3} + d) (b^{4} c^{6} - b^{2} c^{3} d + d^{2})