# Expansions-10

### From Homeworkwiki

**If a + b + c = 0 , then show that a ^{ 3 } + b ^{ 3 } + c ^{ 3 } = 3 a b c**

**Solution :**

Given, a + b + c = 0

=> a + b = - c

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

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

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

=> a ^{ 3 } + b ^{ 3 } + c ^{ 3 } - 3 a b c = 0

Therefore, **a ^{ 3 } + b ^{ 3 } + c ^{ 3 } = 3 a b c **