因数 8c^3-27d^3

解

因数

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

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

解答ステップ

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

指数の規則を適用する

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

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

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

簡素化

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

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