因数 27f^3g^3-64h^3j^3

解

因数

27 f^{3} g^{3} - 64 h^{3} j^{3}

(3 f g - 4 jh) (9 f^{2} g^{2} + 12 j f g h + 16 j^{2} h^{2})

解答ステップ

27 f^{3} g^{3} - 64 h^{3} j^{3}

27 f^{3} g^{3}

を書き換え

(3 f g)^{3}

64 h^{3} j^{3}

を書き換え

(2^{2} hj)^{3}

= (3 f g)^{3} - (2^{2} hj)^{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 f g)^{3} - (2^{2} hj)^{3} = (3 f g - 2^{2} hj) ((3 f g)^{2} + 3 f g 2^{2} hj + (2^{2} hj)^{2})

= (3 f g - 2^{2} hj) ((3 f g)^{2} + 3 f g 2^{2} hj + (2^{2} hj)^{2})

簡素化

(3 f g - 2^{2} hj) ((3 f g)^{2} + 3 f g \cdot 2^{2} hj + (2^{2} hj)^{2}) : (3 f g - 4 jh) (9 f^{2} g^{2} + 12 j f g h + 16 j^{2} h^{2})

= (3 f g - 4 jh) (9 f^{2} g^{2} + 12 j f g h + 16 j^{2} h^{2})