因数 27a^3b^3-8c^3d^3

解

因数

27 a^{3} b^{3} - 8 c^{3} d^{3}

(3 ab - 2 c d) (9 a^{2} b^{2} + 6 ab c d + 4 c^{2} d^{2})

解答ステップ

27 a^{3} b^{3} - 8 c^{3} d^{3}

27 a^{3} b^{3}

を書き換え

(3 ab)^{3}

8 c^{3} d^{3}

を書き換え

(2 c d)^{3}

= (3 ab)^{3} - (2 c d)^{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})

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

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

簡素化

(3 ab - 2 c d) ((3 ab)^{2} + 3 ab \cdot 2 c d + (2 c d)^{2}) : (3 ab - 2 c d) (9 a^{2} b^{2} + 6 ab c d + 4 c^{2} d^{2})

= (3 ab - 2 c d) (9 a^{2} b^{2} + 6 ab c d + 4 c^{2} d^{2})