因数 27x^3-64x^3

解

因数

27 x^{3} - 64 x^{3}

- 37 x^{3}

解答ステップ

27 x^{3} - 64 x^{3}

27 x^{3}

を書き換え

(3 x)^{3}

64 x^{3}

を書き換え

(2^{2} x)^{3}

= (3 x)^{3} - (2^{2} x)^{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 x)^{3} - (2^{2} x)^{3} = (3 x - 2^{2} x) ((3 x)^{2} + 3 x 2^{2} x + (2^{2} x)^{2})

= (3 x - 2^{2} x) ((3 x)^{2} + 3 x 2^{2} x + (2^{2} x)^{2})

簡素化

(3 x - 2^{2} x) ((3 x)^{2} + 3 x \cdot 2^{2} x + (2^{2} x)^{2}) : - 37 x^{3}

= - 37 x^{3}