展開する (c^2-3bd+12ae)^3

解

展開する

(c^{2} - 3 b d + 12 a e)^{3}

c^{6} - 9 c^{4} b d + 36 e c^{4} a + 27 c^{2} b^{2} d^{2} + 432 e^{2} c^{2} a^{2} - 216 e c^{2} b d a - 27 b^{3} d^{3} + 1728 e^{3} a^{3} - 1296 e^{2} b d a^{2} + 324 e b^{2} d^{2} a

解答ステップ

(c^{2} - 3 b d + 12 a e)^{3}

= (c^{2} - 3 b d + 12 e a)^{3}

(c^{2} - 3 b d + 12 a e)^{3} = (c^{2} - 3 b d + 12 a e) (c^{2} - 3 b d + 12 a e) (c^{2} - 3 b d + 12 a e)

= (c^{2} + 12 e a - 3 b d) (c^{2} + 12 e a - 3 b d) (c^{2} + 12 e a - 3 b d)

拡張

(c^{2} - 3 b d + 12 a e) (c^{2} - 3 b d + 12 a e) (c^{2} - 3 b d + 12 a e) : c^{6} - 9 c^{4} b d + 36 e c^{4} a + 27 c^{2} b^{2} d^{2} + 432 e^{2} c^{2} a^{2} - 216 e c^{2} b d a - 27 b^{3} d^{3} + 1728 e^{3} a^{3} - 1296 e^{2} b d a^{2} + 324 e b^{2} d^{2} a

= c^{6} - 9 c^{4} b d + 36 e c^{4} a + 27 c^{2} b^{2} d^{2} + 432 e^{2} c^{2} a^{2} - 216 e c^{2} b d a - 27 b^{3} d^{3} + 1728 e^{3} a^{3} - 1296 e^{2} b d a^{2} + 324 e b^{2} d^{2} a