zs

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

受欢迎的代数 >

化简 (b-c)^3+(c-a)^3+(a-b)^3

解答

化简

(b - c)^{3} + (c - a)^{3} + (a - b)^{3}

解答

- 3 b^{2} c + 3 b c^{2} - 3 c^{2} a + 3 c a^{2} - 3 b a^{2} + 3 b^{2} a

求解步骤

(b - c)^{3} + (c - a)^{3} + (a - b)^{3}

展开

(b - c)^{3} : b^{3} - 3 b^{2} c + 3 b c^{2} - c^{3}

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

展开

(c - a)^{3} : c^{3} - 3 c^{2} a + 3 c a^{2} - a^{3}

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

展开

(a - b)^{3} : a^{3} - 3 b a^{2} + 3 b^{2} a - b^{3}

= b^{3} - 3 b^{2} c + 3 b c^{2} - c^{3} + c^{3} - 3 c^{2} a + 3 c a^{2} - a^{3} + a^{3} - 3 b a^{2} + 3 b^{2} a - b^{3}

同类项相加:

- c^{3} + c^{3} = 0

= b^{3} - 3 b^{2} c + 3 b c^{2} - 3 c^{2} a + 3 c a^{2} - a^{3} + a^{3} - 3 b a^{2} + 3 b^{2} a - b^{3}

同类项相加:

- a^{3} + a^{3} = 0

= b^{3} - 3 b^{2} c + 3 b c^{2} - 3 c^{2} a + 3 c a^{2} - 3 b a^{2} + 3 b^{2} a - b^{3}

对同类项分组

= b^{3} - b^{3} - 3 b^{2} c + 3 b c^{2} - 3 c^{2} a + 3 c a^{2} - 3 b a^{2} + 3 b^{2} a

同类项相加:

b^{3} - b^{3} = 0

= - 3 b^{2} c + 3 b c^{2} - 3 c^{2} a + 3 c a^{2} - 3 b a^{2} + 3 b^{2} a

流行的例子

- 3 x^{2} + 12 x - 9 = 0

2 x^{2} + 5 x + 3 < 0

8 x - 2 = 0

8 x^{2} = 12 x + 4

4(x-4)=19-7(4x+1)

4 (x - 4) = 19 - 7 (4 x + 1)