# Expansions-4

### From Homeworkwiki

**If a ^{ 2 } + b ^{ 2 } + c ^{ 2} = 29 and a + b + c = 9, find : a b + b c + ca**

**Solution:**

Since, (a + b + c) ^{ 2 } = a ^{ 2 } + b ^{ 2 } + c ^{ 2 } + 2 ( a b + b c + c a )

Therefore, ( 9 ) ^{ 2 } = 29 + 2 ( a b + b c + c a )

=> 81 - 29 = 2 ( a b + b c + c a )

Therefore, **( a b + b c + c a )** = 52 / 2 = **26**