What is expand (a+b-c)^3 ?

The solution to expand (a+b-c)^3 is a^3+3a^2b-3a^2c+3ac^2+3bc^2+3ab^2-c^3-3b^2c-6abc+b^3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

expand (a+b-c)^3

expand

(a + b - c)^{3}

a^{3} + 3 a^{2} b - 3 a^{2} c + 3 a c^{2} + 3 b c^{2} + 3 a b^{2} - c^{3} - 3 b^{2} c - 6 ab c + b^{3}

Solution steps

(a + b - c)^{3}

Simplify

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

= (a + b - c) (a + b - c) (a + b - c)

Expand

(a + b - c) (a + b - c) : a^{2} + 2 ab - 2 a c + b^{2} - 2 b c + c^{2}

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

Distribute parentheses

= a^{2} a + a^{2} b + a^{2} (- c) + 2 aba + 2 abb + 2 ab (- c) - 2 a c a - 2 a c b - 2 a c (- c) + b^{2} a + b^{2} b + b^{2} (- c) - 2 b c a - 2 b c b - 2 b c (- c) + c^{2} a + c^{2} b + c^{2} (- c)

Simplify

a^{2} a + a^{2} b + a^{2} (- c) + 2 aba + 2 abb + 2 ab (- c) - 2 a c a - 2 a c b - 2 a c (- c) + b^{2} a + b^{2} b + b^{2} (- c) - 2 b c a - 2 b c b - 2 b c (- c) + c^{2} a + c^{2} b + c^{2} (- c) : a^{3} + 3 a^{2} b - 3 a^{2} c + 3 a c^{2} + 3 b c^{2} + 3 a b^{2} - c^{3} - 3 b^{2} c - 6 ab c + b^{3}

= a^{3} + 3 a^{2} b - 3 a^{2} c + 3 a c^{2} + 3 b c^{2} + 3 a b^{2} - c^{3} - 3 b^{2} c - 6 ab c + b^{3}

5 \frac{5}{8}

(3 a - 5 b + 3 c) (4 a + 2 b + c)

(- 4)^{2} + (- 4)^{2}

(5 x^{2} + 5 x - 8) + (- 2 x^{2} + 3 x - 2)

\frac{14}{32}

What is expand (a+b-c)^3 ?
The solution to expand (a+b-c)^3 is a^3+3a^2b-3a^2c+3ac^2+3bc^2+3ab^2-c^3-3b^2c-6abc+b^3